Question

A customer from cavallaro's fruit stand picks a sample of 5 oranges at random from a crate containing 60 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: 0.379

Step-by-step explanation:

Given : Total oranges =60

Rotten oranges = 6

Number of fresh orange = 60-6=54

Sample size : n=5

Customer picks up 5 oranges from total 60, then the probability that first orange is fresh =$\dfrac{54}{60}$

Probability that next orange is fresh= $\dfrac{54-1}{60-1}=\dfrac{53}{59}$ and so on.....

The probability that more than one are rotten :-

$1-\text{P(no rotten)}\\\\=1-\dfrac{54\times53\times52\times51\times50}{60\times58\times57\times56\times55}\\\\=1-0.621166945577\\\\=0.378833054423\approx0.379$

Answer 2

Chances of one or more = 1 - chance of no rotten oranges

chance of no rotten oranges = 54/60 * 53/59 * 52/58 * 51/57 * 50/56