[Junoon - E - Jee] - Probability - 13th Nov.pdf

Taught 1 Million+ Students
Certified by the IAPT
EdTech Patent Holder
Director - Unacademy JEE/NEET
CEO & Founder, Factovation
AIR-9 CENTA TPO - Challenger Math
12+ yrs Teaching experience
Purnima Kaul
IIT-BHU B.Tech, M.Tech - Math & Computing

Unacademy
Subscription
LIVE Polls & Leaderboard
LIVE Doubt Solving
LIVE Interaction
LIVE Class Environment Performance Analysis
Weekly Test Series
DPPs & Quizzes

India’s BEST Educators Unacademy Subscription
If you want to be the BEST
“Learn” from the BEST

Bratin Mondal
100 %ile
Top Results
Amaiya Singhal
100 %ile

12th / Drop
11th / 9, 10
PURNIMA
MAX

Random Experiment
Experiment in which satisfies the following conditions:
1. It should have more than one outcome
2. Outcomes are non-predictable

It are the set of all possible outcomes of an random experiment
S = {H, T}
S = {HH, HT, TH, TT}
S = {1, 2, 3, 4, 5, 6}
Sample Space

(i) Face Cards:
(ii) Honours Cards:
(iii) Knave Cards:
K, Q and J
10, J and Q
A, K, Q and J

Number of elements in sample space if n Dices are thrown ?
Random Experiment n(S)
1 Dice are thrown
2 Dice are thrown
3 Dice are thrown
.
.
.
n Dice are thrown

A coin is tossed. If head appears, another coin is tossed otherwise, a
dice is thrown. Write down the sample of the experiment.

Event
Events are the subset of sample space
Getting an odd outcome in throwing dice.
S = {1, 2, 3, 4, 5, 6}
A = {1, 3, 5}

Complement of an Event
The complement of an event ‘A’ with respect to a sample space S are
the set of all elements of ‘S’ which are not in A. It are usually
denoted by A’, Ā or AC.
P(A) + P(Ā) = 1

Classical
Definition of
Probability

P(A) =
Number of favorable outcomes
Total Number of Outcomes
0 ≤ P(A) ≤ 1
Classical Definition of Probability

Number of unfavorable cases
Odds in favour of an event =
Number of favorable cases
Number of favorable cases
Odds against in an event =
Number of unfavorable cases
Odds in Favour and Odd Against

1 2 3 4 5 6
1 (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
2 (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
3 (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
4 (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
5 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
6 (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
Outputs
of
the
Second
Dice
Outputs of the First Dice

A pair of fair dice are rolled. Find the odds against getting a total
greater than 9.

Two dices are rolled. If both dices have six faces numbered 1, 2, 3, 5,
7 and 11, then the probability that the sum of the numbers on the top
faces is less than or equal to 8 is :
A. 4/9
B. 17/36
C. 5/12
D. 1/2

A card is drawn randomly from a well shuffled pack of 52 cards. The
probability that the drawn card is
1. Heart
2. Face card
3. Heart and face card
4. Heart or face card
5. neither a heart nor a face card

Words with or without meaning are to be formed using all the letters
of the word Examination. The probability that the letter M appears at
the fourth position in any such word is:
A. 1/66
B. 1/11
C. 1/9
D. 2/11
(20 July 2021 Shift 1)

(20 July 2021 Shift 1)
Let 9 distinct balls be distributed among 4 boxes, B1, B2, B3 and B4.
If the probability than B3 contains exactly 3 balls is k Then k
is lies in the set:
A.
B.
C.
D.

(16 Mar 2021 Shift 2)
Let A denote the event that a 6 - digit integer formed by 0, 1, 2, 3,
4, 5, 6 without repetitions, be divisible by 3. Then probability of
event A is equal to :
A. 9/56
B. 4/9
C. 3/7
D. 11/27

(26 Feb shift 2)
A seven digit number is formed using digit 3, 3, 4, 4, 4, 5, 5. The
probability, that number so formed is divisible by 2, is :
A. 6/7
B. 4/7
C. 3/7
D. 1/7

(JEE Main 2020 6 sep)
Out of 11 consecutive natural numbers if three numbers are
selected at random (without repetition), then the probability that
they are in A.P with positive common difference, is :
A. 5/101
B. 10/99
C. 5/33
D. 15/101

Examples
1. Getting 7 on a throw of single dice (Impossible)
2. Getting a number less than 7 on a throw of single dice (Sure)
Impossible and Sure Events

Simple Event Compound Event
n(E) = 1 n(E) > 1
RE: Tossing 2 coins
A : getting both heads
RE: Tossing 2 coins
B : getting at least one head

Equally Likely
Mutually Exclusive/Disjoint
Exhaustive
Types of Events

Events are equally likely if they have same probability of occurrence.
Example:
1. ‘Getting odd outcome’ and ‘getting even outcome’ in single throw of a fair
dice.
2. ‘Getting head’ and ‘getting tail’ on the toss of fair Dice.
Equally Likely

Two events A and B are said to be mutually exclusive or disjoint if their
simultaneous occurrence are impossible
If A and B are mutually exclusive then A ∩ B = ɸ
Example:
RE: throwing a dice
A: getting odd number
B: getting even number
Mutually Exclusive / Disjoint

Question 1:
RE: throwing a dice
A: getting prime number
B: getting even number
C: getting multiple of 3
Question 2:
RE: drawing one card from a pack of 52 cards
A: getting ace
B: getting red card
Mutually Exclusive / Disjoint

Events whose union are equal to sample space
If A, B and C are exhaustive then A U B U C = S
Example:
RE: Throwing a dice
A: getting even number
B: getting prime number
C: getting number less than 4
Exhaustive Events

Two events A and B are independent if occurrence or non occurrence of A has
no effect on occurrence or non occurrence of B
Example:
1. A dice are thrown and a Dice are thrown, than getting even number on
dice and getting head on Dice are independent
2. If it rains then crop will be good (dependent)
Dependent and Independent Events

(JEE Adv. 2013)
Four persons independently solve a certain problem correctly with
probabilities 1/2, 3/4, 1/4, 1/8. Then the probability that the
problem are solved correctly by at least one of them are
A. 235/256
B. 21/256
C. 3/256
D. 253/256

(JEE M 2019)
Four persons can hit a target correct with probabilities
1/2, 1/3, 1/4, 1/8. If all hit at the target independently, then the
probability that the target would be hit, are
A. 25/192
B. 7/32
C. 1/192
D. 25/32

Addition
theorem on
Probability

A B
P(at least one event will occur)
= P(AUB)
= P(A) + P(B) - P(A ∩ B)
1.

A B
P(exactly one event will occur)
= P(A) + P(B) - 2 P(A∩B)
2.

A B
P(only A occurs)
= P(A) - P(A∩B)
3.

I. If A and B are mutually exclusive events then
P(A ∪ B) = P(A) + P(B) {∵P(A ⋂ B) = 0}
II. If A and B are exhaustive events then P(A ∪ B) = 1
Note:

(JEE 2008)
A die are thrown. Let A be the event that the number obtained are
greater than 3. Let B be the event that the number obtained are
less than 5. Then P(A ∪ B) are
A. 3/5
B. 0
C. 1
D. 2/5

If A and B are two events associated with an experiment then
1. P(A U B) are probability of occurrence of at least one event
2. P(A ∩ B) are probability of occurrence of both A and B
3. P(A) are probability of occurrence of A
4. P(B) are probability of occurrence of B
A B
P(A U B) = P(A) + P(B) - P(A ∩ B)
Addition theorem on Probability

(JEE Main 2020 - 8 Jan)
Let A and B be two events such that the probability that exactly
one of them occurs is 2/5 and the probability that A or B occurs is
1/2 , then the probability of both of them occur together is
A. 1/10
B. 2/9
C. 1/8
D. 1/12

A B
C
P(A ∪ B ∪ C)=
P(A) + P(B) + P(C) - P(A ∩ B) - P(B ∩ C) - P(A ∩ C) + P(A ∩ B ∩ C)
1.

I. If A, B and C are mutually exclusive events then
P(A ∪ B ∪ C) = P(A) + P(B) + P(C)
II. If A and B are exhaustive events then P(A ∪ B ∪ C) = 1
Note:

A B
C
P(exactly two events A, B, C occur)
= P(A ∩ B) + P(A ∩ B) + P(A ∩ B) - 3 P(A ∩ B ∩ C)
2.

A B
C
P(exactly one of the events A, B, C occur)
P(A) + P(B) + P(C) - 2P(A ∩ B) - 2P(B ∩ C) - 2P(A ∩ C) + 3P(A ∩ B ∩ C)
3.

(JEE M 2017)
For three events A, B and C
P(Exactly one of A or B occurs) = P (Exactly one of B or C occurs)
= P(Exactly one of C or A occurs) = 1/4 and
P(All the three events occur simultaneously) = 1/16
Then the probability that at least one of the events occurs, are:
A. 3/16
B. 7/32
C. 7/16
D. 7/64

(JEE Main 2020 6 Sep)
The probabilities of three events A, B and C are given by P(A) = 0.6,
P(B) = 0.4 and P(C) = 0.5 if P(A U B) = 0.8, P(A ⋂ C) = 0.3,
P(A ⋂ B ⋂ C) = 0.2, P(B ⋂ C) = β and P(A U B U C) = α, where 0.85 ≤ α ≤ 0.95,
then β lies in the interval :
A. [0.25, 0.35]
B. [0.35, 0.36]
C. [0.36, 0.40]
D. [0.20, 0.25]

(JEE Adv.)
If M and N are any two events , then which one of the following represents
the probability of the occurrence of exactly one of them?
A. P(M) + P(N) - 2P(M ∩ N)
B. P(M) + P(N) - (M ∩ N)

(JEE 2003)
If P(B) = 3/4, P(A∩B∩C) = 1/3 and P(Ā∩C ∩ B) = 1/3, then
P(B ∩ C) are
A. 1/12
B. 1/6
C. 1/15
D. 1/9

A: “odd outcome” = {1, 3, 5}
B: “Prime outcome” = {2, 3, 5}
S: Sample space = {1, 2, 3, 4, 5, 6}
Illustration

Let A and B be two events associated with a same sample space S. the
conditional probability of an event A given B, where B has already
occurred, are denoted as
And are defined as
Definition

Roll a fair die twice. Let A be the event that the sum of the two rolls
equals six, and let B be the event that the same number comes up
twice. What are P(A/B)
A. 1/6 B. 5/36
C. 1/5 D. None

Let A and B be two events such that P(A) = 0.3, P(B) = 0.6 and
Then equals
A. 3/4
C. 9/40
B. 5/8
D. 1/4

Let X and Y be two events such that P(X) = 1/3 , P(X/Y) = 1/2 and
P(Y/X) = 2/5, then which of the following is/are corect:
A. P(Y) = 4/15
C. P(X ∩ Y) = 1/5
B. P(X’ | Y) = 1/2
D. P(X ∪ Y) = 2/5
(JEE Adv. 2017)

Multiplication
Theorem
on Probability

Multiplication Theorem
1. P(A ∩ B) = P(A). P(B/A)

Multiplication Theorem
1. If A and B be two independent events, then P(A ∩ B) = P(A).P(B)
2. If A and B be two independent events, then P(A/B) = P(A)

If A and B be independent events, then (A and B’), (A’ and B) and (A’ and B’)
are also independent events.
P(A ∩ B’) = P(A).P(B’)
P(A’ ∩ B) = P(A’).P(B)
P(A’ ∩ B’) = P(A’).P(B’)
Note :

Independent Events
If A, B and C be three independent events, then P(A ∩ B ∩ C) = P(A). P(B). P(C)

If A, B and C be pairwise independent events, then
Pair-wise Independent Events

(JEE Main 2020 - 8 Jan)
Let A and B be two independent events such that
Then, which of the following is True ?
A.
B.
C.
D.

Let A and B be two events such that P(A ∪ B) = 1/6, P(A ∩ B) = 1/4, and
P(A) = 1/4, where A stands for complement of event A. then events A
and B are
A. Equally likely and mutually exclusive
B. Equally likely but not independent
C. Independent but not equally likely
D. Mutually exclusive and independent
(JEE 2005, 2014)

(JEE Adv. 2011)
Let E and F be two independent events. The probability that exactly
one of them occurs are 11/25 and the probability of none of them
occurring are 2/25. If P(T) denoted the probability of occurrence of
the event T, then
A. P(E) = 4/5, P(F) = 3/5 B. P(E) = 1/5, P(F) = 2/5
C. P(E) = 2/5, P(F) = 1/5 D. P(E) = 3/5, P(F) = 4/5

(JEE Adv. 2019)
Let S be the sample space of all 3 x 3 matrices with entries from the
set {0, 1}. Let the events E1 and E2 be given by E1 = {A ∈ S : det A = 0}
and E2 = {A ∈ S : sum of entries of A are 7}. If a matrix are chosen at
random from S, then the conditional probability P(E1/E2) equals
____.

(JEE Adv. 2012)
Let X and Y be two events such that P(X | Y) = 1/2, P(Y/X) = 1/3, and
P(X ∩ Y) = 1/6 . Which of the following are (are) correct?
A. P(X ∪ Y) = 2/3
B. X and Y are independent
C. X and Y are not independent
D. P(Xc ∩ Y) = 1/2

(JEE Adv. 2017)
Let X and Y be two events such that P(X) = 1/3. P(X|Y) = 1/2 and
P(Y|X) = 2/5. Then
A. P(Y) = 4/15 B. P(X’|Y) = 1/2
C. P(X ∩ Y) = 1/5 D. P(X ∪ Y) = 2/5

(JEE Adv. 2017)
A six faced fair die are thrown until 1 comes, then the probability that 1
comes in even number of trails are
A. 5/11
C. 6/11
B. 5/6
D. 1/6

A pair of unbiased dice are rolled together till a sum of “either 5 or 7”
are obtained. Then find the probability that 5 comes before 7.
A. 5/11
C. 6/11
B. 5/6
D. 2/5

Paragraph Question 1
A fair die are thrown repeatedly until a six are obtained. Let X denote
the number of toss required.
The probability that X = 3 equals
A. 25/216
C. 5/36
B. 25/36
D. 125/216
(2009)

(2009)
The probability that X ≥ 3 equals
A. 125/216 B. 25/36
C. 5/36 D. 25/216

The probability of a man hitting a target is 1/10 The least number of
shots required, so that the probability of his hitting the target at least
once is greater than 1/4 , is

In a game, two players A and B take turns in throwing a pair of fair
dice starting with player A and total of scores on the two dice, in
each throw is noted. A wins the game if he throws a total of 6 before
B throws a total of 7 and B wins the game if he throws a total of 7
before A throws a total of six. The game stops as soon as either of
the players wins. The probability of A winning the game is :
A. 5/31 B. 31/61 C. 5/6 D. 30/31

→ Fair
→ Doubly headed
→ Weighted
Example 1:
A box contains three coins, one fair, one two-headed, and one is weighted such
that (P(H) = ⅓ ). A coin is selected at random and thrown. Find the probability that
head appears.

Let E1, E2, …...En be n mutually exclusive and exhaustive events, with non-
zero probabilities, of a random experiment. If A be any arbitrary event of
the sample space of the above random experiment with P(A) > 0, then
Total Probability Theorem

→ Fair
→ Doubly headed
→ Weighted
Example 1:
A box contains three coins, one fair, one two-headed, and one is weighted such
that (P(H) = ⅓ ). A coin is selected at random and thrown. Given that head
appears, find the probability that coin was fair.

If an event A can occur only with one of the n pairwise mutually exclusive
and exhaustive events B1, B2, ….Bn & if the conditional probabilities of the
events.
P(A/B1), P(A/B2) …… P(A/Bn) are known the,
Bayes Theorem

Bag A contains 3 white and 2 black balls. Bag B contains 2 white
and 2 black balls. One ball are drawn at random from A and
transferred to B. One ball are selected at random from B and are
found to be white. The probability that the transferred ball are
white are
A. 8/13
C. 4/13
B. 5/13
D. 9/13

In a factory which manufactures bolts, machines A, B and C
manufacture respectively 25%, 35% and 40% of the bolts. Of their
outputs, 5, 4 and 2 percent are respectively defective bolt. A
bolts are drawn at random from the product and are found to be
defective. What are the probability that it are manufactured by
the machine B?

In a group of 400 people, 160 are smokers and non-vegetarian; 100
are smokers and vegetarian and the remaining 140 are non-
smokers and vegetarian. Their chances of getting a particular
chestinongo disorder are 35%, 20% and 10% respectively. A person
is chosen from the group at random and is found to be suffering
from the chest disorder. The probability that the selected person is
a smoker and non-vegetarian is:
A. 7/45 B. 8/45 C. 14/45 D. 28/45

In a test, an examinee either guesses or copies or knows the
answer for a multiple choice question having FOUR choices of
which exactly one are correct. The probability that he makes a
guess are 1/3 and the probability for copying are 1/6. The
probability that hare answer are correct, given that he copied it are
1/8. The probability that he knew the answer, given that hare
answer are correct are
A. 5/29
C. 24/29
B. 9/29
D. 20/29

Let an experiment has n-independent trials, and each of the trial
has two possible outcomes
I. Success
II. Failure
p → Probability of getting success
q → Probability of getting failure
such that p + q = 1
Then, P(Exactly r successes) = P(X = r) = nCr pr qn-r
Binomial probability

A pair of dice are thrown 6 times, getting a doublet are considered
success. Compute the probability of
1. No success
2. Exactly one success
3. At least one success
4. At most one success

In a hurdle race a man has to clear 9 hurdles. Probability that he
clears a hurdle 2/3 and the probability that he knocks down the
hurdle are 1/3. Find the probability that he knocks down less than 2
hurdles.

A drunkard takes a step forward or backward. The probability that
he takes a step forward are 0.4. Find the probability that at the end
of 11 steps he are one step away from the starting point.

A multiple choice examination has 5 questions. Each question
has three alternative answers of which exactly one are correct.
The probability that a student will get 4 or more correct answers
just by guessing are:
A. B. C. D.
(JEE M 2013)

(2011)
Consider 5 independent Bernoulli trials each with probability of
success p. If the probability of at least one failure are greater
than or equal to 31/32, then p lies in the interval.
A. B. C. D.

(18 Mar 2021 Shift 2)
Let in a Binomial distribution, consisting of 5 independent trials,
probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048
respectively. Then the probability of getting exactly 3 successes is
equal to:
A. 32/625
B. 80/243
C. 40/243
D. 128/625

(26 Feb Shift 1)
A fair coin is tossed a fixed number of times. If the probability of
getting 7 heads is equal to probability of getting 9 heads, then the
probability of getting 2 heads is :
A.
B.
C.
D.

(JEE Adv. 2020)
The probability that a missile hits a target successfully are 0.75. In
order to destroy the target completely, at least three successful
hits are required. Then the minimum number of missiles that have
to be fired so that the probability of completely destroying the
target are NOT less than 0.95, are _____.

Probability
Distribution
Table

(JEE Adv. 2020)
Three balls are drawn one by one without replacement from a bag
containing 5 white and 4 red balls. Find the probability distribution
of the number of red balls drawn.

(JEE M 2019)
Two cards are drawn successively with replacement from a well-
shuffled deck of 52 cards. Let X denote the random variable of
number of aces obtained in the two drawn cards.
Then P(X = 1) + P(X = 2) equals:
A. 49/169 B. 52/169 C. 24/169 D. 25/169

Binomial
Probability
Distribution

Let an experiment has n independent trials and each of the trial has two possible
outcomes i.e. success or failure.
If random variable (Xi) = number of successes
then probability of getting exactly ‘r’ successes are P(X = r) = nCr pr.qn-r
where p = probability of success
and q = probability of failure
Binomial Probability Distribution (BPD)

X = number of successes
Binomial Probability Distribution Table

Mean of BPD :
Variance of BPD :
Standard Deviation of BPD :

(JEE M 2017)
A. 6/25
A box contains 15 green and 10 yellow balls. If 10 balls are randomly
drawn, one-by-one, with replacement, then the variance of the
number of green balls drawn are:
B. 12/5 C. 6 D. 4

( 2004)
The mean and the variance of a binomial distribution are 4 and 2
respectively. Then the probability of exactly 2 successes are
A. 28/256 B. 219/256 C. 128/256 D. 37/256

1. One-dimensional Probability:
P =
Favourable length
Total length
2. Two-dimensional Probability:
P =
Favourable area
Total area
3. Three-dimensional Probability:
P =
Favourable volume
Total volume
L
l
A
a
v
V
Geometrical probability (Continuous sample space)

A point are taken inside a circle of radius r find the probability that
the point are closer to the centre as a circumference.

A point are selected randomly inside a equilateral triangle whose
length are 3. Find the probability that its distance from any corner
are greater than 1.

Two players of equal skill A and B are playing a game. They leave
off playing (due to some force majeure conditions) when A wants 3
points and B wants 2 to win. If the prize money are Rs. 16000/-. How
can the referee divide the money in a fair way.

If p1 and p2 are the probabilities of speaking the truth of two
independent witnesses A and B who give the same statement
P (both speaks truth/ Statements Match) =
p1p2
p1p2 + (1 - p1) (1 - p2)
Coincidence Testimony

A speaks truth 3 times out of 4, and B 7 times out of 10. They both
assert that a white ball has been drawn from a bag containing 6
balls of different colours; find the probability of the truth of their
assertion.

A speaks the truth 3 out of 4 times, and B 5 out of 6 times. What are
the probability that they will contradict each other in stating the
same fact.
A. 4/5 B. 1/3 C. 7/20 D. 3/20

A man are known to speak the truth 3 out if 4 times. He throws a die
and reports that it are a six. The probability that it are actually a six
are
A. 3/8 B. 1/5 C. 3/4 D. None of these

Homework
Questions
Solutions will be discussed on Nov 16, 6pm on
Unacademy app.

A man are known to speak the truth 3 out if 4 times. He throws a die
and reports that it are a six. The probability that it are actually a six
are
A. 4/5 B. 1/5 C. 7/20 D. 3/20

A. 1/12 B. 2/12 C. 7/12 D. 5/12
If A and B are two events such that

A. 7/16 B. 7/64 C. 3/16 D. 7/32
For three events A, B and C, P (Exactly one of A or B occurs) = P(Exactly
one of B or C occurs) = P(Exactly one of C or A occurs)
= 1/4 and P(All the three events occurs simultaneously) = 1/16 Then the
probability that at least one of the events occurs, is

A. 7/16 B. 7/64 C. 3/16 D. 7/32
For three events A, B and C, P (Exactly one of A or B occurs) = P(Exactly
one of B or C occurs) = P(Exactly one of C or A occurs) = 1/4 and
P(All the three events occurs simultaneously) = 1/16 Then the probability
that at least one of the events occurs, is

The chance of an event happening is square of chance of second event
happening but the odds against first is cube of odds against the second.
Find chances of events

Three numbers are chosen at random without replacement from
{1, 2, …., 8}. The probability that their minimum is 3, given that their
maximum is 6, is
A. 3/8 B. 1/5 C. 1/2 D. 2/3

Two integers are selected at random from a set {1, 2, .... , 11}. Given that
the sum of selected numbers is even, the conditional probability that both
the numbers are even is:
A. 7/10 B. 1/2 C. 2/5 D. 3/5

A. 1/12 B. 1/20 C. 10/13 D. 13/200
A and B are two students. Their probabilities of solving a
problem correctly are1/4 and 1/5 respectively. If the probability of their
making a common error is 1/40 and they obtain
the same answer, then the probability of their answer is correct is

A. 2, 4, or 8 B. 3, 6, or 9 C. 4 or 8 D. 5 or 10
An experiment has 10 equally likely outcomes. Let A and B be two
non-empty events of the experiment. If A consists of 4 outcomes,
the number of outcomes that B must have so that A and B are
independent, is

Four persons independently solve a certain problem correctly with
probabilities 1/2, 3/4, 1/4, 1/8. Then, the probability that the
problem is solved correctly by at least one of them, is
A. 235/256 B. 21/256 C. 3/256 D. 253/256

Ram plays 3 games of chess with Shyam. Probability that Ram wins it 0.5,
that he loses is 0.3 while for tie its 0.2. Find the probability that Ram wins
exactly 2 games

A person goes to office either by car, scooter, bus or train, probability of
which being 1/7, 3/7, 2/7 and 1/7 respectively. Probability that he reaches
office in time, if he takes car, scooter, bus or train is7/9, 8/9, 5/9 and 8/9
respectively. Find the probability that he reaches office in time.
A. 4/9 B. 4/7 C. 5/9 D. 7/9

Box 1 contain 5 white & 2 black balls while Box 2 contain 3 white & 4
black balls. A ball is randomly drawn from Box 1 & is shifted to Box 2.
Now a ball is drawn from Box 2, find the probability that its black.
A. 13/36 B. 15/58 C. 19/35 D. 15/28

A bag contains 4 red and 6 black balls. A ball is drawn at random
from the bag, its colour is observed and this ball along with two
additional balls of the same colour are returned to the bag. If now a
ball is drawn at random from the bag, then the probability that this
drawn ball is red, is
A. 3/10 B. 2/5 C. 1/5 D. 3/4

A bag contains 4 red and 6 black balls. A ball is drawn at random
from the bag, its colour is observed and this ball along with two additional
balls of the same colour are returned to the bag. If now a ball is drawn at
random from the bag, then the probability that this drawn ball is red, is

A student answers a multiple choice question with 5 alternatives, of which
exactly one is correct. The probability that he knows the correct answer is p,
0 < p < 1. If he does not know the correct answer, he randomly ticks one
answer. Given that he has answered the question correctly, the probability
that he did not tick the answer randomly, is
A. B. C. D.

A signal which can be green or red with probability 4/5 and 1/5
respectively, is received by station A and then transmitted to station B. The
probability of each station receiving the signal correctly is 3/4 If the signal
received at station B is green, then the probability that the original signal
was green is
A. B. C. D.

A box contains 24 identical balls of which 12 are white and 12 are black. The
balls are drawn at random from the box one at a time with replacement.
Find the probability that a white ball is drawn for the fourth time on 7th
draw?

A multiple choice examination has 5 questions. Each question has three
alternative answers of which exactly one is correct. The probability that a
student will get 4 or more correct answers just by guessing is
A. B. C. D.

For an initial screening of an admission test, a candidate is given fifty
problems to solve. If the probability that the candidate can solve any
problem is 1/4 then the probability that he is unable to solve less than two
problems is :
A. B. C. D.

If X is a Binomial variate with the range {0, 1, 2, 3, 4, 5, 6} and
P(X = 2) = 4P(X = 4), then the parameter p of X is
A. 1/3 B. 1/2 C. 2/3 D. 3/4

Let a random variable X have a binomial distribution with mean 8 & variance 4
If , then k is equal to.

A random variable X has the following probability distribution:
X 1 2 3 4 5
P(x) K2
2K K 2K 5K2
Then P(x > 2) is equal to:
A. 23/36 B. 7/12 C. 1/36 D. 1/6

हज़ारो सुक
ू न छोड़ने पड़ते
हैं एक जुनून क
े लिए !

[Junoon - E - Jee] - Probability - 13th Nov.pdf

Recommended

Recommended

More Related Content

Similar to [Junoon - E - Jee] - Probability - 13th Nov.pdf

Similar to [Junoon - E - Jee] - Probability - 13th Nov.pdf (20)

Recently uploaded

Recently uploaded (20)

[Junoon - E - Jee] - Probability - 13th Nov.pdf