Question

The probability of a machine being accidentally overfilled on a given day is 0.05. If the machine is overfilled there is a 0.8 probability that it will break down dur ing the course of the day. If the machine is not overfilled the probability of a breakdown during the day is only 0.1. Yesterday the machine broke down. What is the probability that it had been accidentally overfilled

Answer 1

0.2963 or 29.63%

Explanation:

There are two possibilities for a machine breaking down:

1 - Overfilled and broke down (O&B)

2- Not overfilled and broke down (N&B)

The probabilities for each outcome are as follows;

`P(O\&B) = 0.05*0.8\\P(O\&B) = 0.04\\`

`P(N\&B) = (1-0.05)*0.1\\P(N\&B) = 0.095\\`

Given that the machine broke down, the probability that it was overfilled is:

`P(O|B) =(P(O\&B))/(P(O\&B)+P(N\&B))\\P(O|B) =(0.04)/(0.04+0.095)\\P(O|B) =0.2963=29.63\%`

The probability is 0.2963 or 29.63%.