A batch of 500 containers for frozen orange juice contains 5 that are defective.
ID: 3200714 • Letter: A
Question
A batch of 500 containers for frozen orange juice contains 5 that are defective. Two are selected, at random, without replacement from the batch. What is the probability that the second one selected is defective given that the first one was defective? What is the probability that both are defective? What is the probability that both are acceptable? Three containers are selected, at random, without replacement, from the batch. What is the probability that the third one selected is defective given that the first and second ones selected were defective? 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? What is the probability that all three are defective?Explanation / Answer
a) Selecting a defective from remaining 699 with 4 defective,
Required probability = 4/ 699
b) Selecting 2 from 700 can be done in 700C2 ways
Selecting 2 from 5 defective can be done in 5C2 ways
Required probability = 5C2 / 700C2
= 1/24465
c) Selecting 2 from 700 can be done in 700C2 ways
Both are acceptable 695C2 ways
Required probability = 695C2 / 700C2
= 0.9857
d) Selecting a defective from remaining 698 with 3 defective,
Required probability = 3C1 / 698C1
= 0.004
e) Selecting a defective from remaining 698 with 4 defective,
Required probability = 4C1/ 698C1
= 0.005
f) All 3 are decective
Required probability = 5C3 / 700C3
= 1/ 5692190
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