Question

A customer from Cavallaro's Fruit Stand picks a sample of 5 oranges at random from a crate containing 65 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

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Answer 2

To solve this problem, we can use the complement rule.

The probability that the sample contains 1 or more rotten oranges is equal to 1 minus the probability that the sample contains no rotten oranges.

The probability of picking one orange that is not rotten is (65 - 6) / 65 = 59 / 65.

The probability of picking five oranges that are not rotten is (59/65)^5.

Therefore, the probability of the sample containing no rotten oranges is (59/65)^5.

Hence, the probability of the sample containing 1 or more rotten oranges is:

1 - (59/65)^5 = 0.461 (rounded to three decimal places)

Therefore, the probability that the sample contains 1 or more rotten oranges is 0.461.