Question

A machine produces small cans that are used for baked beans. The probabil- ity that the can is in perfect shape is 0.9. The probability of the can having an unnoticeable dent is 0.02. The probability that the can is obviously dented is 0.08. Produced cans get passed through an automatic inspection machine, which is able to detect obviously dented cans and discard them. What is the probability that a can that gets shipped for use will be of perfect shape?

Answer 1

0.9783 = 97.83% probability that a can that gets shipped for use will be of perfect shape

Explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Shipped for use

Event B: Perfect shape

Probability of being shipped for use:

Perfect shape(0.9 probability) or unnoticeable dent(0.02 probability). So

`P(A) = 0.9 + 0.02 = 0.92`

Being shipped for use and being in perfect shape.

0.9 probability, so
`P(A \cap B) = 0.9`

What is the probability that a can that gets shipped for use will be of perfect shape?

`P(B|A) = (P(A \cap B))/(P(A)) = (0.9)/(0.92) = 0.9783`

0.9783 = 97.83% probability that a can that gets shipped for use will be of perfect shape