An electronic unit contains three independent modules and connected in series (the…

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

Problem

An electronic unit contains three independent modules

A,\,B

and

C

connected in series (the unit functions only if every module functions). The probabilities that each module functions during a specified time are

P(A)=0.98,\;P(B)=0.95

and

P(C)=0.90

. (i) Find the probability that the unit functions. (ii) Given that the unit has failed, calculate the probability that module

C

was the cause of failure. (iii) Module

C

is replaced by a new module

D

that functions with probability

0.94

. Keeping

A

and

B

unchanged, determine the new probability that the unit functions and comment on the improvement obtained.