Question

The probability that a customer's order is not shipped on timeis 0.05. A particular customer places three orders, and the ordersare placed far enough apart in time that they can be considered tobe independent events. Round the answers to 3 significantdigits.a) What is the probability that all are shipped on time?b) What is the probability that exactly one is not shipped ontime?c) What is the probability that two or more orders are notshipped on time?

Answer 1

Explanation:

Given that the three orders are independent of each other.

X - no of ships not shipped on time

X is binomial with p = 0.05 and q = 0.95, n = 3

a) the probability that all are shipped on time=
`0.95^3 =0.854`

b) the probability that exactly one is not shipped ontime

=P(X=1) =
`3C1(0.05)(0.95)^2 = 0.135`

c) the probability that two or more orders are notshipped on time

`= P(X=2)+P(x=3)\\= 1-P(x=0)-P(x=1)\\=1-0.854-0.135\\=0.011`