Given:
Total students = 100
Two sections are formed of sizes 40 and 60
You and your friend are two particular students among the 100
Total possible cases:
After you are placed in a section, your friend can go into any of the remaining 99 positions.
So, total possible cases = 99
(a) Probability that both enter the same section
Case 1: You are in the section of 40 students
Remaining students in that section = 39
Case 2: You are in the section of 60 students
Remaining students in that section = 59
Total favourable cases =
39 + 59 = 98
Probability =
98 / 99
(b) Probability that both enter different sections
Favourable cases =
Total cases − Same section cases
= 99 − 98
= 1
Probability =
1 / 99
Final Answers:
(a) Probability that both enter the same section = 98 / 99
(b) Probability that both enter different sections = 1 / 99
Two dice are thrown. The events A, B and C are as follows:
A: getting an even number on the first die.
B: getting an odd number on the first die.
C: getting the sum of the numbers on the dice ≤5.
State true or false: (give reason for your answer)
(i) A and B are mutually exclusive
(ii)A and B are mutually exclusive and exhaustive
(iii) A=B′
(iv)A and C are mutually exclusive
(v)A and B′ are mutually exclusive.
(vi) A′,B′,C are mutually exclusive and exhaustive.
From the employees of a company, \(5\) persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows: A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over \(35\) years?