A batch of 500 containers for frozen orange juice contains 5 that are

Edmund Adams

Edmund Adams

Answered question

2021-11-15

A batch of 500 containers for frozen orange juice contains 5 that are defective. Two are selected, at random, without replacement from the batch. 
1) What is the probability that the second one selected is defective given that the first one was defective? 
2) What is the probability that both are defective? 
3) What is the probability that both are acceptable?

Answer & Explanation

Greg Snyder

Greg Snyder

Beginner2021-11-16Added 11 answers

Step 1
(1) A batch of 500 containers for frozen orange juice contains 5 that are defective. Two are randomly selected without replacement.
Let x1 is defined as first one defective, and x2 is defined as second one defective.
The probability that the second one selected is defective given that the first one was defective is,
P(x2x1)=P(x2x1)P(x1)
=(5500)×(4499)(5500)
=4499
=0.0080
Thus, the probability that the second one selected is defective given that the first one was defective is 0.0080.
Step 2
2) The probability that both are defective is,
P(x2x1)=(5500)×(4499)
=20249,500
=0.00008
thus, the probability that both are defective is 0.00008.
3) The probability that both are acceptable is,
P(x2x1)=(495500)×(494499)
=244,530249,500
=0.98008
thus, the probability that both are acceptable is 0.98008.

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