Question

A machine shop has 100 drill presses and other machines in constant use. The probability

that a machine will become inoperative during a given day is 0.002. During some days, no

machines are inoperative, but on other days, one, two, three, or more are broken down.

What is the probability that fewer than two machines will be inoperative during a

particular day?

Answer 1

Math mode activated

Explanation:

The number of machines that become inoperative during a given day follows a binomial distribution with parameters n = 100 (the number of machines) and p = 0.002 (the probability that a machine will become inoperative).

The probability that fewer than two machines will be inoperative during a particular day is the sum of the probabilities that zero or one machine will be inoperative. This can be calculated using the binomial probability mass function as follows:

P(X < 2) = P(X = 0) + P(X = 1)

= (100 choose 0) * (0.002)^0 * (1 - 0.002)^100 + (100 choose 1) * (0.002)^1 * (1 - 0.002)^99

= 1 * 1 * 0.817 + 100 * 0.002 * 0.818

= 0.817 + 0.164

= 0.981

Therefore, the probability that fewer than two machines will be inoperative during a particular day is approximately 0.981.