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
A die is thrown. Describe the following events:
(i) \(A: a\) number less than \(7\)
(ii) \(B: a\) number greater than \(7\)
(iii) \(C: a\) multiple of \(3\)
(iv) \(D: a\) number less than \(4\)
(v) \(E: a\) even number greater than \(4\)
(vi) \(F: a\) number not less than \(\)\(3\)
Also, find \(A∪B, A∩B, B∪C, E∩F, D∩E, A-C, D-E, E∩F', F'\)
An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events: \(A:\) the sum is greater than \(8\), \(B:\)\(2\) occurs on either die \(C:\)The sum is at least \(7\), and a multiple of \(3\). Which pairs of these events are mutually exclusive?