A batch of 427 containers for frozen orange juice contains 3 that are defective.

Question

A batch of 427 containers for frozen orange juice contains 3 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 (e.g. 98.76543). 0.00747 b) What is the probability that both are defective? Round your answer to seven decimal places (e.g. 98.7654321). 0.0000330 c) What is the probability that both are acceptable? (e.g. 98.765). 0-9859814 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? (e.g. 98.765). 0.0023 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 (e.g. 98.76543). 0.0047 f) What is the probability that all three are defective? (e.g. 98.765). 0.014

Explanation / Answer

Let X shows the number of defectives in sample. Here X has hypergeometric distribution with following parameters:

Population size: N = 427

Number of defectives in population: k = 3

Sample size: n =2

(a)

After selecting the first one defective number of defectives remaining is 2 out of 426 so required probability is

2 /426 = 0.00469

(b)

The probability that both are defective is

(3/427) * (2/426) = 0.0000330

(c)

Both are acceptable is

(424/427)*(423/426)=0.98598

(d)

After selecting the first two defectives number of defectives remaining is 1 out of 425 so required probability is

1 /425 = 0.002

(e)

The required probability is

2/425 = 0.00471

(f)

(3/427)*(2/426)*(1/425) = 0.000

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