Mr Adam and Mr Ouyang interviewed 75 students and found that 35 were in favor of changing date for Exam

Question

a)If Mr Persaud selects 5 students and surveys them, what is the probability that more students are in favor of changing the date?

 

b)What is the expected number of students who want Exam date changed?

Answer 1

A.  The probability that any specific student is in favor of changing the date is 35/75 = 7/15.  And the probability that a specific student is NOT in favor would be 1 minus that, or 8/15.

 

In order for more students in the sample of 5 to be in favor, that would mean either 3, 4, or 5 students would have to be in favor.  So let's find the probability that exactly each of those numbers (3, 4, or 5) would be in favor.  Since those numbers are mutually exclusive (e.g., you can't have exactly 3 students in favor AND exactly 4 students in favor), we can just add the probabilities together.  So...

 

The probability of 3 students being in favor is ₃C₅ * (7/15)³ (8/15)² = 0.289

 

The probability of 4 students being in favor is ₄C₅ * (7/15)⁴ (8/15)¹ = 0.126

 

The probability of 5 students being in favor is ₅C₅ * (7/15)⁵ (8/15)⁰ = 0.022

 

The sum is 0.437, so that is the probability of more students being in favor than being opposed.

 

B. The expected number of students who are in favor is equal to the probability of one student being in favor, times the number of students, which is 7/15 * 5 = 7/3 = 2.333