Question

A batch of 500 containers for frozen orange juice contains 5 that are defective. Three 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?

b. What is the probability that the first two selected are defective?

c. What is the probability that the first two selected are both acceptable?

d. What is the probability that the third one selected is defective given that the first and second ones selected were defective?

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?

f. What is the probability that all three selected ones are defective?

Answer 1

a)

probability that the second one selected is defective given that the first one was defective

=4/499 =0.00802 (since there remain 4 defective from 499 if first is defective)

b)

probability that the first two selected are defective =(5/500)*(4/499)=0.000080

c)

probability that the first two selected are both acceptable =(495/500)*(494/499)=0.98008

d)

probability that the third one selected is defective given that the first and second ones selected were defective =(3/498)=0.00602 (since there remains 2 defective from 498 if first 2 are defective()

e)

probability that the third one selected is defective given that the first one selected was defective and the second one selected was okay =(4/498)=0.008032

f)

probability that all three selected ones are defective =(5*4*3)/(500*499*498)=0.000000483