# ISRO-2013-69, UGCNET-Dec2012-III: 62

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If a program $P$ calls two subprograms $P1$ and $P2$ and $P1$ can fail $50$% of the time and $P2$ can fail $40$% of the time, what is the failure rate of program $P$?

1. $50$%
2. $60$%
3. $70$%
4. $10$%
• 🚩 Edit necessary | | 💬 “Correct answer is (c) 70% while in GateOverflow answer key it is given (d) 10%, please correct the key.”
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Assume we run this program 100 times.

50 times it fails at p1 and only 50 times the control reaches to p2.

and P2 fails at 40 %

40% of 50 is 20

Therefore out of 100 times it fails 70 times....

Program P fails when either P1 fails or P2 fails, i.e. failure of P1 + failure of P2.

But this will also contain the case when both P1 and P2 fails at the same time, i.e. failure of P1 ∩ failure of P2, since this case will be already be counted on (P1+P2).

Therefore, our final answer will be failure of P1 + failure of P2 - (failure of P1 ∩ failure of P2)

= $\left ( \frac{50}{100} \right )$ + $\left ( \frac{40}{100} \right )$ -$\left ( \frac{50}{100} * \frac{40}{100}\right )$

= $\left ( \frac{90}{100} \right )$ - $\left ( \frac{2000}{10000} \right )$

= $\left ( \frac{90}{100} \right )$ - $\left ( \frac{20}{100} \right )$

= $\left ( \frac{70}{100} \right )$

= 70%

selected by

P1: fails 50% time. Success 50% time....0.5

P2: fails 40% time. Success 60% time.... 0.6

Success rate = both p1 and p2 wins = 0.5x0.6= 0.3

Failure rate =1- success rate = 1-0.3 =0.7=

70%

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You have answered it in a very good way, Shiva. I am very happy to read your solution.Thanks.

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