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

Answer 1

The failure rate of program p is $\bf{70\%}$

Explanation:

Program p fails only when either subprogram p1 fails or subprogram p2 fails such as failure of p1 + failure of p2.  

There is one case when both of the subprograms P1 and P2 fail at the same instant of time, given by failure of p1 $\cap$ failure of p2.

Subprogram p1 failure rate is 50% thus Success rate of p1 is 50% time i.e 0.5

Subprogram p2 failure rate is 40% thus Success rate of p2 is 60% time i.e 0.6

According to probability,

failure of p1 + failure of p2 - (failure of p1 $\cap$ failure of p2)

Hence, equation is $p((p1 \cup p2))= p1+p2-(p1*p2)$

$=( \frac{50}{100} ) + ( \frac{40}{100}) - ( \frac{50}{100} \times \frac{40}{100})$

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

$= ( \frac{70}{100})$

$=\bf{70\%}$

Thus, the failure rate of program p is $\bf{70\%}$