A system contains three independent components

MATHEMATICS · Single correct · A Level · Mathematics · Probability · Probability

Problem

A system contains three independent components. Components

A

and

B

are connected in parallel, and this parallel combination is connected in series with component

C

. The probabilities that

A

B

and

C

work are

0.7

0.8

and

0.9

respectively. What is the probability that the system works? (a) 0.504 (b) 0.940 (c) 0.846 (d) 0.154