Question

Elly's Hotdog Emporium is famous for its chilidogs. Elly's latest sales indicate that 30% of the customers order their chilidogs with hot peppers. Suppose 15 customers are selected at random.

a. What is the probability that exactly 10 customers will ask for hot peppers?
b. What is the probability that between two and six people inclusive want hot peppers?
c. What is the probability that all 15 will want hot peppers?

Answer 1

A.) 0.002980

B.) 0.8335

C.) 0.00000000143

Explanation:

The problem can be solved using the binomial probability formula :

P(success) p = 0.3

Number of trials (n) = 15

P(x = x) = nCx * p^x * (1 - p)^(n-x)

A) Exactly 10:

P(x = 10) = 15C10 * 0.3^10 * 0.7^5

3003 * 0.3^10 * 0.7^5

= 0.002980

B) between 2 and 6 people :

Using binomial probability calculator to save time

P(2) + p(3) + p(4) + p(5) + p(6)

0.0915 + 0.170 + 0.219 + 0.206 + 0.147

= 0.8335

C.) What is the probability that all 15 will want hot peppers?

P(x = 15) = 15C15 * 0.3^15 * 0.7^0

= 1 * 1.4348907E−8 * 1

= 0.00000000143