Answer to Question #338923 in Statistics and Probability for Andy

Question

At a suburban shopping mall 70% of customers pay by ecocash.Find the probability that in a randomly selected sample of ten customers : exactly 3 pay by ecocash and more than 6 pay by ecocash

Answer 1

Let $X=$ the number of customers pay by ecocash:$X\sim Bin(n, p).$

Given $n=10, p=0.7, q=1-p=0.3.$

1.

$$P(X=3)=\dbinom{10}{3}(0.7)^{3}(0.3)^{10-3}=0.009001692$$

2.

$$P(X>6)=1-P(X=7)-P(X=8)$$

$$-P(X=9)-P(X=10)$$

$$=1-\dbinom{15}{7}(0.7)^{7}(0.3)^{10-7}-\dbinom{15}{8}(0.7)^{8}(0.3)^{10-8}$$

$$-\dbinom{15}{9}(0.7)^{9}(0.3)^{10-9}\dbinom{15}{10}(0.7)^{10}(0.3)^{10-10}$$

$$=0.6496107184$$