An item manufactured in a factory must pass three successive quality checks

MATHEMATICS · Multi-part · A Level · Mathematics · Probability · Probability

Problem

A

B

and

C

. The probabilities associated with these checks are as follows:

P(A)=0.90

P(B\mid A)=0.95

P(C\mid A\cap B)=0.97

. Assume that an item reaches check

C

only if it has cleared both

A

and

B

. (i) Calculate the probability that an item clears all three checks. (ii) If an item has cleared checks

A

and

B

, find the probability that it fails check

C

. (iii) If an item is found to have cleared check

C

, determine the probability that it had in fact cleared check

A