The Environmental Protection Agency (EPA) has contracted with your company for equipment to monitor water quality for several lakes in your water district. A total of 10 devices will be used. Assume that each device has a probability of 0.01 of failure during the course of the monitoring period.

a. What is the probability that none of the devices fail?

b. What is the probability that two or more devices fail?

c. If the EPA requires the probability that none of the devices fail to be at least 0.95, what is the largest individual failure probability allowable?

Answer :

Step 1 of 4 :

Given, An Environmental Protection Agency(EPA) has contracted with a company for several lakes in your water district.

Total of 10 devices used and we have to assume that each device has probability of 0.01

Let X follows Binomial distribution with n=10 and p = 0.01

B(n.p) = , where, x = 0, 1, 2, . . . . , 10.

Step 2 of 4 :

the claim is to find the probability that none of the device failThen , P(x) = , where, x = 0, 1, 2, . . . . , 10

The probability none of the device fail is x = 0.

Thus, P(x = 0) =

= (1)

= 0.90438

Therefore, the probability of none of the device fail is 0.90438.