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? Choices:	A) 9/80	B) 3/10	C) 261/800	D) 35/80	E) 497/800
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   261/800
<result>C</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, 1/8; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails?