Question

The probability that the first stage of a numerically controlled machining operation for high-rpm pistons meets specifications is 0.90. Failures are due to metal variations, fixture alignment, cutting blade condition, vibration, and ambient environmental conditions. Given that the first stage meets specifications, the probability that a second stage of machining meets specifications is 0.95. What is the probability that both stages meet specifications?

Answer 1

There is an 85.5% probability that both stages meet specifications.

Explanation:

We have these following probabilities:

A 90% probability that the first stage meets specifications.

If the first stage meets specifications, a 95% probability that the second stage also meets specifications.

What is the probability that both stages meet specifications?

This is the multiplication of these probabilities. So:

`P = 0.9*0.95 = 0.855`

There is an 85.5% probability that both stages meet specifications.