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

Question

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 $P$?

• A. $50$%
• B. $60$%
• C. $70$%
• D. $10$%

Comments

An intuitive  way of thinking about this problem is the following

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....

Answer 1

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%

Answer 2

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%

Comments

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