Question

A company has 200 machines. Each machine has a 12% probability of not working. If you were to pick 40 machines randomly, the probability that 5 would not be working is __________.

a) 0.025

b) 0.075

c) 0.105

d) 0.145

Answer 1

c) 0.105 indicating a 10.5% probability that exactly 5 out of the 40 randomly selected machines will not be working. This calculation demonstrates the likelihood of encountering a specific number of non-functioning machines when selecting 40 machines at random from the total pool of 200.

Explanation:

The probability that 5 out of 40 randomly picked machines will not be working can be calculated using the binomial probability formula. In this case, the probability of one machine not working is 12%, which implies a probability of 88% (1 - 0.12) that a machine will be working. Using the binomial probability formula, the calculation involves determining the probability of exactly 5 out of 40 machines not working. This is found using the formula:
`\({{40}\choose{5}} * (0.12)^5 * (0.88)^(35)\).`Solving this equation results in approximately 0.105, indicating a 10.5% chance that exactly 5 out of 40 machines selected at random will not be working.

Each machine has a 12% probability of not working, which translates to an 88% probability of it working (1 - 0.12 = 0.88). The probability of 5 machines out of 40 not working is calculated using the binomial probability formula
`: \({{40}\choose{5}} * (0.12)^5 * (0.88)^(35)\).`This calculation yields approximately 0.105, indicating a 10.5% probability that exactly 5 out of the 40 randomly selected machines will not be working. This calculation demonstrates the likelihood of encountering a specific number of non-functioning machines when selecting 40 machines at random from the total pool of 200.