2.0
Probability
LECTURE
1
Introduction
2.0
Nishant Vora
B.Tech - IIT-Patna
7+ years Teaching experience
Mentored 5 lac+ students
Teaching Excellence Award
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Random Experiment
Experiment in which satisfies the following conditions
1. It should have more than one outcome
2. Outcomes are non predictable
Examples of Random Experiment
Sample Space
It is 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}
Write a sample space of three coins are tossed ?
Write a sample space of four coins are tossed ?
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
Number of elements in sample space if n coins are tossed ?
Outputs of the first Dice
Outputs of the Second Dice
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)
Number of elements in sample space if 3 dice are thrown?
Example
A coin is tossed. If head appears another coin is tossed otherwise a dice
is thrown. Write down the sample space of the experiment.
Event
It is the subset of sample space
Example
Getting an odd outcome in throwing dice.
A = {1, 3, 5}
S = {1, 2, 3, 4, 5, 6}
Classical Definition of Probability
P(A) =
Number of favorable outcomes
Total Number of Outcomes
0 ≤ P(A) ≤ 1
Complement of an Event
The complement of an event ‘A’ with respect to a sample space
S is the set of all elements of ‘S’ which are not in A. It is usually
denoted by A’, Ā or AC.
P(A) + P(Ā) = 1
2 Dice
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Find the Probability of getting sum of 7 if a pair of dice is thrown
Example
An old man while dialing a seven digit telephone number, after
having dialed the first five digits, suddenly forgets the last two. But
he remembered that the last two digits were different. On this
assumption he randomly dials the last two digits. What is the
probability that the correct telephone number is dialed.
A. 1/90
B. 1/100
C. 1/99
D. 1/50
Example
4 identical apples and 3 oranges are randomly placed in a line.
Find the chances that the extreme fruits are both oranges.
A. 1/6
B. 2/7
C. 1/7
D. 3/7
Example
Two natural are randomly selected from the set of first 20 natural
numbers. Find the probability that
(A) their sum is odd
(B) Sum is even
Example
A leap year is selected at random. Find the probability that it has
(A) 53 sundays
(B) 53 Sundays and Mondays
(C) 53 Sundays or 53 Mondays
Concept:
Leap year has 366 days = 52 weeks 2 days
Example
What is the chance that the fourth power of an integer chosen randomly
ends in the digit six.
A. 4/10
B. 3/10
C. 1/10
D. 6/10
Example
5 different marbles are placed in 5 different boxes randomly. Find the
probability that exactly two boxes remain empty. Given each box can
hold any number of marbles.
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