Statistics

Harbour:

The proportion of graduating students in a certain discipline who wait for three months before getting employed for the first time is 41%. If 9 fresh graduates from the discipline are taken at random, what is the probability that

(a) exactly four (b) between 2 and 5 inclusive (c) at least 3 wait for three months before getting jobs.

This is a combination question.
P(more than 3 months to get a job) = 0.41 p=0.41
P(getting a job before 3 months ) = 0.59 q = 0.59

P(exactly 4 out of 9 take longer) = 9C4 * 0.41 ⁴ * 0.59 ⁵

P(between 2 and 5 inclusive wait longer) = [9C2 * 0.41 ² * 0.59 ⁷] + [9C3 * 0.41 ³ * 0.59 ⁶] + [9C4 * 0.41 ⁴ * 0.59 ⁵] + [9C5 * 0.41 ⁵ * 0.59 ⁴]

P(at least 3 wait 3 months) = P( 3,4,5,6,7,8 or 9 wait 3 months) = 1 - P(only 0,1 or 2 people wait 3 months)
= 1 - [ 9C0 * 0.41 ⁰ * 0.59 ⁹ + 9C1 * 0.41 ¹ * 0.59 ⁸ + 9C2 * 0.41 ² * 0.59 ⁷ ]
= 1 - [ 0.59 ⁹ + 9 * 0.41 * 0.59 ⁸ + 9C3 * 0.41 ³ * 0.59 ⁶ ]