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.

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24-03-2017
Mathematics

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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.

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Аноним Аноним · Answer 1 · 2017-03-24T13:06:21+01:00

Аноним Аноним

24-03-2017

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

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JeanaShupp JeanaShupp · Answer 2 · 2019-10-15T18:42:35+02:00

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 =[tex]\dfrac{54}{60}[/tex]

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

The probability that more than one are rotten :-

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