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

Answer:

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

Step-by-step 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) =

$=\dfrac{6}{75} = 0.08$

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.