1. ## Probabilities

A sensitive machine is tuned correctly for 95% of the time. If the machine is correctly tuned, the probability of a spoilt product is 1%; if not, it is 40%. The first product of a test run is inspected and found to be satisfactory.

What is the probability that the machine had been correctly tuned?

2. Originally Posted by gibonwa33
A sensitive machine is tuned correctly for 95% of the time. If the machine is correctly tuned, the probability of a spoilt product is 1%; if not, it is 40%. The first product of a test run is inspected and found to be satisfactory.

What is the probability that the machine had been correctly tuned?
We need to use conditional probabilities here.
P(Machine correctly tuned | product not faulty) = 0.95 * 0.99/(0.95 * 0.99 + 0.05 * 0.6)

=~ 0.97

where
0.95 * 0.99 = Prob of Machine correctly tuned and product not being faulty
denominator = Overall Probability of the machine being non faulty