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?
A)0.0200
B)0.1637
C)0.8187
D)0.9824

Question

Quizplus · Accepted Answer

The probability that fewer than two machines will be inoperative can be found by calculating the probability of no machines breaking down plus the probability of exactly one machine breaking down. This is a binomial probability problem where n = 100, p = 0.002, and we are interested in k = 0 and k = 1.The probability of no machines breaking down (k=0) is given by the binomial formula: $P(X=0) = \binom{100}{0} (0.002)^0 (1-0.002)^{100-0} = (1)(1)(0.998)^{100}$.The probability of exactly one machine breaking down (k=1) is: $P(X=1) = \binom{100}{1} (0.002)^1 (1-0.002)^{100-1} = (100)(0.002)(0.998)^{99}$.Adding these two probabilities gives the total probability of fewer than two machines breaking down, which is approximately 0.9824.

A Machine Shop Has 100 Drill Presses and Other Machines