Question

An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known: P(A fails) = 0.2 P(B fails alone) = 0.15 P(A and B fail) = 0.15 Evaluate the following probabilities (i) P(A fails| B has failed) (ii) P(A fails alone)

Answer 1

(i)

Let E A be the event that subsystem A fails and E B be the event that subsystem B fails.

Now the probabilities are defined as,

P( E A )=0.2 P( E A  and  E B )=0.15

The probability of occurrence of event E B is calculated as,

P( E B )=P( B fails alone )+P( E A  and  E B ) P( E B )=0.15+0.15 P( E B )=0.3

The probability of failure of subsystem A after failure of subsystem B is,

P( E A | E B )= P( E A  and  E B ) P( E B ) = 0.15 0.3 =0.5

(ii)

Let E A be the event that subsystem A fails and E B be the event that subsystem B fails.

Now the probabilities are defined as,

P( E A )=0.2 P( E A  and  E B )=0.15

The probability of occurrence of event E B is calculated as,

P( E B )=P( B fails alone )+P( E A  and  E B ) P( E B )=0.15+0.15 P( E B )=0.3

The probability that subsystem A fails alone is,

P( A fails alone )=P( E A )−P( E A  and  E B ) =0.2−0.15 =0.05