The document provides an introduction to probability, defining it as the measure of the likelihood of an event occurring and explaining key terminologies like experiments, events, sample space, and complementary events. It illustrates how to express probabilities as fractions using examples, detailing the calculation for multiple events occurring together through 'and' and 'or' scenarios, and emphasizes the concept of independent events. Additionally, the document includes practice questions to reinforce understanding of the probability concepts presented.

1. PROBABILITY
By: Aakanksha jain

2. Introduction
In everyday life, we come across statements such as
• It will probably rain today.
• I doubt that he will pass the test.
• Most probably, Kavita will stand first in the annual
examination.
• There is a 50-50 chance of India winning a toss in
today’s match.
Use: Physical Sciences, Commerce, Biological Sciences, Medical
Sciences, Weather Forecasting, etc

3. History
Blaise Pascal Pierre de Fermat
Chevalier de Mere

4. Definition
✏ Probability is the measure ofhow likely
something will occur.
✏ It is the ratio of desired outcomesto total
outcomes.
✏(# desired) / (# total)
✏ Probabilities of all outcomes sumsto 1.

5. Definitions
Probability is the measure of the likeliness that an event
will occur. Probability is quantified as a number between
0 and 1 (where 0 indicates impossibility and 1 indicates
certainty
• Probability of any event can be expressed as:
0<=P<=1

6. Terminologies
 Experiment: An operation which can produce some
well defined outcomes, is known as experiment.
Trail: performing a experiment is called trail.
E.g. : Tossing a coin
Event: An event is a possible outcome of the
experiment. Like head coming in a toss.
 Remark: Sum of probabilities of all the elementary
events of an experiment is 1.

7. Terminologies
Sample space:
It is a set of all possible outcomes of an experiment.
e.g. when we coin is tossed, the possible outcome are Head and
Tail. So sample space is Head and tail .
The event A’, representing ‘not A’, is called the complement
of the event A. We also say that A’ and A are complementary
events. Also
P(A) +P(A’)=1
 The probability of an event (U) which is impossible to occur
is 0. Such an event is called an impossible event
P(U)=0

8. How do we express probabilities?
Usually, we express probabilities as
fractions.
 The numerator shows the POSSIBLE
number of ways an event can occur.
 The denominator is the TOTAL number
of possible events that could occur.
Let’s look at an example!

9. What is the probability that I will choose a
red marble?
I n this bag of marbles, there are:
• 3 red marbles
• 2 white marbles
• 1 purplemarble
• 4 greenmarbles

10. Ask yourself the following questions:
1. How many red marbles are in the bag?
2. How many marbles are in the bag?
3. If I randomly choose a ball from bag, what
is the probability of getting red ball out of
the bag?
4. If I randomly choose a ball from bag, what
is the probability of getting purple ball out
of the bag?

11. Solution
P E
Number of ways that E can occur
Number of possibilities S
Here E: Our favourable event
S: Total number of outcomes
P(E): Probability of occurrence of our
favourable event

12. Solution
Answer 1: There are 3 red ball in bag.
Answer 2: There are 10 ball in total in bag
Answer 3:Probability of getting red ball from bag,
when we are randomly choosing the ball....
P(Occurrence of red ball) = Total number of red ball present in bag(E)
Total number of balls in bag(S)

13. Solution
P(Occurrence of red ball) = Total number of red ball present in bag(E)
Total number of balls in bag(S
P(Red)=3/10
Answer 4: Probability of getting purple ball out of
bag.
P(Purple)= 1/10

14. Practice
✏ If I flip a coin, what isthe probability
I get heads?
✏ What is the probability I gettails?
✏ Remember, to think of howmany possibilities
there are.

15. Answer
✏ P(heads) =1/2
✏ P(tails) =1/2
✏ If you add these two up, you willget 1,
which means the answers are probably
right.

16. Two or more events
✏ If there are two or more events, you need
to consider if it is happening at the same
time or one after the other.

17. “And”
✏ If the two events are happening at the
same time, you need to multiply the two
probabilities together.
✏ Usually, the questions use the word
“and” when describing the outcomes.

18. The Word And in probability means
Intersection
Q. What is the probability that you roll an
even number and a number greater than 3?
E = rolling an even number
F = rolling a number greater than 3
P(E∩F) = (E∩F) .
Total outcomes

19. Continue...
How can E occur? {2, 4, 6}
How can F occur? {4, 5, 6}
E  F  {2,4,6}{4,5,6}{4,6}
P(E∩F)= 2 = 1
6 3

20. “Or”
✏ If the two events are happening one
after the other, you need to add the two
probabilities.
✏ Usually, the questions use the word “or”
when describing the outcomes.

21. The Word Or in probability means Union
Q. What is the probability that you roll
an even number or a number greater
than 3?
E = rolling an even number
F = rolling a number greater than 3

22. Continue...
P(EUF) = (EUF) .
Total outcomes
How can E occur? {2, 4, 6}
How can F occur? {4, 5, 6}
E UF {2,4,6}U{4,5,6}{2,4,5,6}
P(EUF)= 4 = 2
6 3

23. Practice
✏ If I roll a number cube and flip a coin:
✏ What is the probability I will geta heads
and a 6?
✏ What is the probability I will geta tails or
a 3?

24. Answers
✏ P(heads and 6) = 1/2 x 1/6 =1/12
✏ P(tails or a 5) = 1/2 + 1/6 = 8/12 =2/3

25. Independent Events
Two events are independent if, the outcome OF event
A has no effect on the outcome of event B.
Example: Event A: It rained on Tuesday
Event B: My chair broke at work
These two events are not at all related to each other.
• When we calculate probabilities for independent
events, we always multiply the probabilities.

26. LETS TAKE AN EXAMPLE:
Let Event A:Today it will rain in Delhi.
Event B:Today I will reach office late.
C: FIND Possibility of both events A&B
happening together.
GIVEN: P(A)=0.1,P(B)=0.02
Hence ; P(C)=P(A)*P(B)
=0.1*0.02
=0.002

27. Practice Time
Question 1
A dice is thrown once. What is the probability of getting a
number greater than 4?
Question 2
Cards with numbers 2 to 101 are placed in a box. A card
selected at random from the box. Find the probability that the
card which is selected has a number which is a perfect square.
Question 3
A card is drawn from a well shuffled deck of 52 cards. Find the
probability of getting a joker.

28. Thank you!