Question

12. Assume, in general, that in a species of rodents, there is a probability of 0.52 of being male and probability of 0.48 of being female. Suppose six of these rodents are randomly selected. Determine the probability that exactly three are female.

Answer 1

12)

Let X denote the number of rodents that a female.

Then $X\sim Bin(n=6,p=0.48)$

$P(X=x)=\binom{6}{x}(0.48)^x(1-0.48)^{6-x},x=0,1,2,...,6$

Required probability = $P(X=3)=\binom{6}{3}(0.48)^3(1-0.48)^{6-3}=0.3110$