A cat had a litter of 5 kittens. each sex is equally likely, what is the probability that 3 or less were female kittens?

Question

A. 0.3125

B. 0.5000

C. 0.8125

D. 0.2500

Answer 1

Prob(X=3) = (5 choose 3) (0.5)^3 ( 0.5)^2 = (5*4)/2 * (1/2)^5 = 10/32 = 5/16

Prob(X=2) = (5 choose 2) (0.5)^2 (0.5)^3 = (5*4*3)/(3*2) * (1/2)^5 = 10/32 = 5/16

Prob(X=1) = (5 choose 1) (0.5)^1 ( 0.5)^4 = 5 * (1/2)^5 = 5/32

Prob(X=0) = (5 choose 0) (0.5)^0 (0.5)^5 = (1/2)^5 = 1/32

5/16 + 5/16 + 5/32 + 1/32 = 10/32 + 10/32 + 5/32 + 1/32 = 26/32 = 13/16

The answer is C = 0.8125