Question

20. SAMPLING A customer at Cavallaro's Fruit Stand picks a sample of 3 oranges at random from a crate containing 60 oranges, of which 4 are rotten. What is the probability that the sample contains 1 or more rotten oranges?

Answer 1

19%

Explanation:

First, let's notice that having 1 or more rotten oranges in the sample is the complement of having 0 rotten oranges in the sample. That means

proba (1 or more rotten oranges) + proba (0 rotten oranges) = 100%

We will focus in the case of 0 rotten oranges that's easier and then we go back to this last equation.

For 0 rotten oranges, we need that the customer picks 3 good oranges. As there are 4 rotten oranges in the crate of 60, we have
`60-4=56` good oranges.

So, the customer has a 56/60 chance of getting a good orange. As he needs 3 good oranges at the same time, he has
`(56)/(60) *(55)/(59) *(54)/(60)= (1386)/(1711)` chance.

Therefore, proba(0 rotten oranges) =
`(1386)/(1711)` = 81% (approximately)

Going back to the first paragraph, we have proba(1 or more rotten oranges) = 100% - proba(0 rotten oranges) = 100% - 81% = 19%