Answer:
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.