Question

A company Safety Officer must report to the Plant Manager the status of a hazardous production operation. Each time the operation is performed, historical data shows that there is a 2.1% chance that an injury will occur. If the operation is performed 24 times each shift, what is the probability that an injury will occur exactly one time?

Answer 1

Here, n = 24, p = 0.021, (1 - p) = 0.979 and x = 1
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 1)
P(X = 1) = 24C1 * 0.021^1 * 0.979^23
P(X = 1) = 0.3093