Answer to Question #106195 in Statistics and Probability for DEBORAH SEKYERAA

Question

In 2015,a company estimateted that 65%of its customer were female and, in that year,three customers entered one of their shops. Asuming that these customers were not or acquaintance,fine the probability that they were i) all female ii) all male iii) at least one male

Answer 1

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

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

Given that $p=0.65, n=3$

1) The probability that these customers were all females is

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

2) The probability that these customers were all males is

$$P(X=0)=\binom{3}{0}0.65^0(1-0.65)^{3-0}=$$ $$=1(1)(0.35)^3=0.042875$$

3) The probability that at least one male is

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