Question

A room contains 21 people. 5 are males and the others are female. A random sample of 7 people is drawn without replacement. What is the probability there are fewer than 2 males in the sample?

Round your answer to at least 3 decimal places.

Answer 1

Total number of people = 21

Number of males = 5

Number of females = 21 - 5 = 16

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

P(fewer than 2 males in the sample) = P(0 males in sample) + P(1 male in sample)

= (Number of ways to select 0 males and 7 females + Number of ways to select 1 male and 6 females) / Number of ways to select any 7 people

= (16C7 + 5C1 x 16C6)/21C7

= (11,440 + 5 x 8,008)/116,280

= 0.443