Question

TV studio has brought in 9 boy kittens and 6 girl kittens for a cat food commercial. The director is going to choose 9 of these kittens at random to be in the commercial. What is the probability that the director chooses 5 boy kittens and 4 girl kittens? Round your answer to three decimal places.

Answer 1

Answer:

probability = 0.2517

Step-by-step explanation:

given data

boy kittens = 9

girl kittens = 6

choose kittens at random = 9

solution

total kitten are = 9 + 6 = 15

first we get here total no of probability that is

n(s) = 15 C 9

n(s) = $\frac{15!}{9!(15-9)!}$  

n(s) =5005

and

total way to chose 5 boy kittens is = 9 C 3

n(3) = $\frac{9!}{3!(9-3)!}$  

n(3) =  84

and

total way to chose 4 girl kittens is = 6 C 4

n(4) = $\frac{6!}{4!(6-4)!}$  

n(4) = 15

so

total way to chose 5 boy kittens and 4 girl kittens is

total way = 84 ×15  = 1260

so probability that the director chooses 5 boy kittens and 4 girl kittens is

probability = $\frac{1260}{5005}$  

probability = 0.2517