Question

A customer from Cavallaro's Fruit Stand picks a sample of 4 oranges at random from a crate containing 65 oranges, of which 5 are rotten. What is the probability that the sample contains 1 or more rotten oranges? (Round your answer to three decimal places.)

Answer 1

Let p = proportion of rotten oranges = 5/65 = 0.077

Let X : number of rotten oranges

If n = 4 , we asked P( X 1)

P( X 1) = 1 - P( X = 0)

Using binomial probability

P( X = 0) = n!/ X! * ( n -x)! * p​​​​​​x​​​​​ * ( 1- p)n -x​​​

P( X = 0) = 4!/0!*4! *(0.077)0*(0.923)4

P( X = 0) = 0.7258

P( X 1) = 1 - 0.7258

P( X 1) = 0.274