Question

A University wishes to hire 4 faculty members for its newly established department. They have to select from a group of 8 Male and 7 Female applicants, all of whom are equally qualified to fill in the positions. If University selects 4 at random, what is the probability that:
a) All four will be Men
b) All four will be Women
c) Atleast one will be a Women
d) Atleast one will be a Men

Answer 1

Total No of faculty $= 8 M + 7 F = 15$

 If University selects 4 at random,

a) All four will be Men $= \frac{_8C_4}{_{15}C_4}= \frac{2}{39}$

b) All four will be Women $= \frac{_7C_4}{_{15}C_4}= \frac{1}{39}$

c) At least one will be a Women = 1 - Probability of all men $= 1-\frac{_8C_4}{_{15}C_4}= \frac{37}{39}$

d) At least one will be a Men = 1 - Probability of all women

$= 1-\frac{_7C_4}{_{15}C_4}= \frac{38}{39}$