A class has eight girls and six boys. If the teacher randomly picks six students, what is the probability that he will pick at least two boys?

Question

A class has eight girls and six boys. If the

teacher randomly picks six students, what is

the probability that he will pick at least two

boys?

Answer 1

It is easier to compute the probability of picking 0 or 1 boys, then subtracting from 1.

Let P(x) = probability of picking x boys and the rest girls.

P(0) = (8 / 14) (7 / 13) (6 / 12) (5 / 11) (4 / 10) (3 / 9)

Let C(n,k) = the number of ways k elements can be chosen from among n elements. Same as Combinations.

C(n,k) = n! / (n-k)!

C(6,1) = 6! / 5! = 6 * 5! / 5! = 6

P(1) = 6 * (6 / 14) (8 / 13) (7 / 12) (6 / 11) ( 5 / 10) ( 4 / 9 )

The solution is 1 - P(0) - P(1) = 0.8135