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