A relay has a series of 5 circuits in a line.
A relay has a series of 5 circuits in a line. The even-numbered circuits are control circuits; the odd are buffer circuits. If both a control circuit and the buffer circuit immediately following it both fail in that order, then the relay fails. The probability of circuit one failing is 3/8; circuit two, 1/8; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails?
Answer/Solution
261/800
Steps/Work
The first circuit doesn't matter.
Prob(relay fails) = 1 - Prob(relay succeeds)
Prob(2+3 work) = 1 - 3/80 = 77/80
Prob(4+5 work) = 1 - 3/10 = 7/10
Prob(relay fails) = 1 - Prob(2+3 work AND 4+5 work) = 1 - (77/80)(7/10) = 1 - 539/800 = 261/800
C
Prob(relay fails) = 1 - Prob(relay succeeds)
Prob(2+3 work) = 1 - 3/80 = 77/80
Prob(4+5 work) = 1 - 3/10 = 7/10
Prob(relay fails) = 1 - Prob(2+3 work AND 4+5 work) = 1 - (77/80)(7/10) = 1 - 539/800 = 261/800
C