A machine has two subsystems

MATHEMATICS · Subjective · A Level · Mathematics · Probability · Probability

Problem

A machine has two subsystems,

A

and

B

, connected in parallel. Subsystem

A

consists of two independent components

C_1

and

C_2

connected in series, with working probabilities

0.90

and

0.85

respectively. Subsystem

B

consists of two independent components

C_3

and

C_4

connected in series, with working probabilities

0.80

and

0.75

respectively. Calculate the probability that the machine functions.