Discussion
A program P calls two subprograms P1 and P2. P1 can fail 50% times and P2 40% times. Then P can fail
Answer: D
The program P fails if either of the two subprograms fails. The probability that P1 does not fail is 0.5 and the probability that P2 does not fail is 0.6, so the probability that neither fails is
\[ 0.5 \times 0.6 = 0.3 \]and the program fails in the remaining 1 - 0.3 = 0.7 of the runs, that is 70 per cent, taking the failures to be independent. The figure 50 per cent is the failure rate of P1 alone, 60 per cent has no basis in the data, and 10 per cent is the difference of the rates. The keyed answer is 70%.
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