Question

The business department at a university has 18 faculty members. Of them, 11 are in favor of the proposition that all MBA students should take a course in ethics and 7 are against this proposition. If 5 faculty members are randomly selected from the 18, what is the probability that the number of faculty members in this sample who are in favor of the proposition is exactly two

Answer 1

0.225

Explanation:

Total outcomes of choosing 5 out of 18 members = 18C5

Outcomes of choosing 2 out 11 favourers, 3 out of 7 members = 11C2 & 7C3

Probability = Favourable outcomes / Total outcomes

= ( 11C2 x 7C3 ) / 18C5

[ { 11 ! / 2! 9! } {7 ! / 3! 4! } ]

[ 18 ! / 5! 13! ]

( 55 x 35 ) / 8568

1925 / 8568

= 0.2246 ≈ 0.225