Answer to Question #106178 in Statistics and Probability for Leela Abdulai

Question

in 2015 a company estimated that 65% of its customers were females n ,in that year,3 customers entered 1of the shop's. Assuming that these customers were not related or acquaintances,find the probability that they were
1)All females
2)All male
3)At least one male

Answer 1

Let $X=$ the number of customers who are females: $X\sim B(n;p)$

$$P(X=x)=\binom{n}{x}p^x(1-p)^{n-x}$$

Given that $p=0.65, n=3$

1) The probability that these customers were all females is

$$P(X=3)=\binom{3}{3}0.65^3(1-0.65)^{3-3}=0.274625$$

2) The probability that these customers were all males is

$$P(X=0)=\binom{3}{0}0.65^0(1-0.65)^{3-0}=0.042875$$

3) The probability that at least one male is

$$P(X<3)=1-P(X=3)=1-0.274625=0.725375$$