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, 1/9; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails? Options.
A) 9/80  B) 3/10  C) 303/800  D) 97/300  E) 497/800
The first circuit doesn't matter.   Prob(relay fails) = 1 - Prob(relay succeeds)   Prob(2+3 work) = 1 - 1/30 = 29/30   Prob(4+5 work) = 1 - 3/10 = 7/10   Prob(relay fails) = 1 - Prob(2+3 work AN97/300 4+5 work) = 1 - (29/30)(7/10) = 1 - 203/300 = 97/800   97/300
<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, 1/9; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails?