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, 5/8; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails?
Select the correct option:
A) 9/80
B) 3/10
C) 303/800
D) 69/160
E) 497/800
The first circuit doesn't matter.   Prob(relay fails) = 1 - Prob(relay succeeds)   Prob(2+3 work) = 1 - 3/16 = 13/16   Prob(4+5 work) = 1 - 3/10 = 7/10   Prob(relay fails) = 1 - Prob(2+3 work AN69/160 4+5 work) = 1 - (13/16)(7/10) = 1 -91/160 = 69/160   69/160
<result>D</result>
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, 5/8; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails?