Question

Of the automobiles produced at a particular plant, 40% had a certain defect. a. What is the probability that more than 50 cars will need to be inspected before one with the defect is found? b. What is the probability that the twentieth car inspected will have a defect? c. Suppose a company purchases five of these cars. What is the probability that exactly one of the five cars has a defect?

Answer 1

Let X denotes the number of cars to be inspected before one with the defect is found.

X ~ Geometric(0.4)

The probability mass function of X is

a) The probability that more than 50 cars will need to be inspected before one with the defect is found

B)The probability that the twentieth car inspected will have a defect

c) Let Y denotes the number of cars which has a defect among 5 selected cars.

Y ~ Binomial(n = 5, p = 0.4)

The probability mass function of Y is

The probability that exactly one of the five cars has a defect