Question

A customer from Cavallaro's Fruit Stand picks a sample of 5 oranges at random from a crate containing 75 oranges, of which 6 are rotten. What is the probability that the sample contains 1 or more rotten oranges? (Round your answer to three decimal places.)

Answer 1

0.341 is the probability that the sample contains 1 or more rotten oranges.

Explanation:

We are given the following information:

We treat rotten as a success.

Number of oranges = 75

Number of rotten orange = 6

P(Rotten orange) =

`=(6)/(75) = 0.08`

Then the number of rotten oranges follows a binomial distribution, where

`P(X=x) = \binom{n}{x}.p^x.(1-p)^(n-x)`

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 5

We have to evaluate:

`P(x \geq 1) =1 - P(x = 0)\\\\=1- \binom{5}{0}(0.08)^0(1-0.08)^5\\\\= 1 - 0.659\\= 0.341`

0.341 is the probability that the sample contains 1 or more rotten oranges.