Probability

PROBABILITY
A chance that something will happen.
Sometimes you can measure a probability using words such
as impossible, unlikely, possible, even chance, likely and
certain.

Sample Space
A sample space is the list of all the possible outcomes in a
random experiment.
unpredictable

Example
What is the sample space of tossing a coin?
Head Tail

What is the sample space of tossing a coin twice?

What is the sample space of tossing a coin thrice?

Example
What is the sample space of throwing a die?

What is the sample space of throwing two dice?

PROBABILITY
Deck of Cards
Two colors
Black Red
Four Suits
Clubs Spades Diamonds Hearts

13 Ranks
Ace
Jack Queen King
Digits
Face

Tossing a Coin
When a coin is tossed, there are two possible
outcomes:
We say that the probability of
the coin landing H is ½.
We say that the probability of
the coin landing T is ½.
Head
Tail

Throwing a Die
When a single die is thrown, there are six possible
outcomes: 1, 2, 3, 4, 5, 6.
The probability of any one of
them is 1/6.

PROBABILITY =
number of ways it can happen
total number of outcomes

Example
What is the probability of getting an
even number in throwing a die?
E= 2, 4, 6
S= 1, 2, 3, 4, 5, 6
P=
=
3
6
=
1
2

Example
In throwing two dice, what is the
probability of getting a 3 in at least one
of the dice?
E={ 3,1 , 3,2 , 3,3 , 3,4 , 3,5 , 3,6 ,
1,3 , 2,3 , 4,3 , 5,3 , 6,3 }
P=
=
11
36

Example
What is the probability of getting a sum
of 10 in throwing two dice?
E={ 4,6 , 5,5 , 6,4 }
P=
=
3
36
=
1
12

Example
What is the probability of getting the
same number in throwing two dice?
E={ 1,1 , 2,2 , 3,3 , 4,4 , 5,5 , 6,6 }
P=
=
6
36
=
1
6

Example
Two dice are thrown together. What is
the probability that the sum of the face-
up sides is a prime number?
P=
=
15
36
=
5
12

Example
Find the probability of drawing a “2” of
spades in a standard deck of cards
P=
=
1
52

Example
Find the probability of drawing a jack in
a standard deck of cards
P=
=
4
52
=
1
13

Example
Find the probability of drawing a king of
red colour in a standard deck of cards
P=
=
2
52
=
1
26

Example
Find the probability of drawing a
diamond in a standard deck of cards
P=
=
13
52
=
1
4

Example
Find the probability of drawing a king or
a queen in a standard deck of cards
P=
=
8
52
=
2
13

Example
Find the probability of drawing a non-
face card in a standard deck of cards
P=
=
40
52
=
10
13

Example
Find the probability of drawing a black
face card in a standard deck of cards
P=
=
6
52
=
3
26

Example
Find the probability of drawing a black
card in a standard deck of cards
P=
=
26
52
=
1
2

Example
Find the probability of drawing neither a
heart nor a red king in a standard deck
of cards
P=
=
38
52
=
19
26

Example
Find the probability of drawing neither a
spade nor a jack in a standard deck of
cards
P=
=
36
52
=
9
13

Example
Given a set of 4 cards that includes a
king of spades, a king of hearts, a king
of clubs, and a king of diamonds, two
cards are drawn at the same time. What
is the probability that the cards have the
same colour?

Example
Given a set of 4 cards that includes a king of spades, a king of hearts, a king of clubs,
and a king of diamonds, two cards are drawn at the same time. What is the probability
that the cards have the same colour?
𝐏 =
𝐏 =
2
6
𝐏 =
1
3

Example
cards are drawn one at a time without
replacement. What is the probability
that the cards have the same colour?

Example
and a king of diamonds, two cards are drawn one at a time without replacement. What
is the probability that the cards have the same colour?
𝐏 =
=
4
12
=
1
3

Example
cards are drawn at one at a time,
returning the first card. What is the
probability that the cards have the same
colour?

Example
and a king of diamonds, two cards are drawn at one at a time, returning the first card.
What is the probability that the cards have the same colour?
𝐏 =
=
8
16
=
1
2

Example
There are three blue balls inside an opaque box.
Each ball is numbered from 1 to 3. What is the
probability that a ball with the number “2” on it will
be picked?
P=
=
1
3
1
2
3

Example
probability that a blue ball will be picked?
P=
=
3
3
= 1
1
2
3

Example
probability that a red ball will be picked?
P=
=
0
3
= 0
1
2
3

Example
There are two white and three red balls inside an
opaque box. In drawing two balls one at a time
without replacement, what is the probability of
getting two red balls?
R2W2
W1
R1
R3

Example
There are two white and three red balls inside an opaque box. In drawing two balls
one at a time without replacement, what is the probability of getting two red balls?
R3
W
2
W
1
R1
R2
W
2
W
1
R1 R2
R3
R3
W
2
W
1
R1
R2W
2
W
1
R1
R2 R3
W
1
W
2
R1 R2
R3
𝐏 =
=
6
20
=
3
10

Example
There are two white and three red balls inside an
opaque box. In drawing two balls one at a time
and returning the first ball in the box, what is the
probability of getting a white ball in the first draw
and a red ball in the second draw?
R2W2
W1
R1
R3

Example
There are two white and three red balls inside an opaque box. In drawing two balls
one at a time and returning the first ball in the box, what is the probability of getting a
white ball in the first draw and a red ball in the second draw?
R3
W
2
R1
R2
W
1
R1 R2
R3
R3
W
2
W
1
R2
W
2
W
1
R1
R3
W
1
W
2
R1 R2
W
1
W
1
W
2
W
2
R1
R1
R2
R2
R3
R3
𝐏 =
=
6
25

Example
A bag contains 30 balls out of which 15 are red
balls, 𝑤 are white balls, and 𝑔 are green balls.
The probability of getting a white ball is twice the
probability of getting a green ball. Find the
number of white balls and green balls?

Probability

More Related Content

Similar to Probability

Recently uploaded

Probability