A batch of 410 containers for frozen orange juice contains 7 that are defective.

Question

A batch of 410 containers for frozen orange juice contains 7 that are defective. Two are selected, at random, without replacement from the batch.

a) What is the probability that the second one selected is defective given that the first one was defective? Round your answer to five decimal places

b) What is the probability that both are defective? Round your answer to seven decimal places.

c) What is the probability that both are acceptable? Round your answer to three decimal places.

Three containers are selected, at random, without replacement, from the batch.

d) What is the probability that the third one selected is defective given that the first and second one selected were defective? Round your answer to three decimal places

e) What is the probability that the third one selected is defective given that the first one selected was defective and the second one selected was okay? Round your answer to five decimal places.

f) What is the probability that all three are defective? Round your answer to three decimal places

Explanation / Answer

(According to Chegg policy, only four subquestions will be answered. Please post the remaining in another question)

a) The probability that an orange juice is defective = 7/410

Since the first one was defective, the probability that the second is defective = 6/409 = 0.01467

b) The probability that the first one is defective = 7/410

The probability that the second juice is defective = 7/410

=> Probability = 7/410 * 7/410 = 0.00029

c) The probability that a juice is acceptable = 403/410

=> Probability that both are acceptable = (403/410)2 = 0.96615

d) Since the first two were defective, the probability that the third is also defective = 5/408 = 0.01225

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