Question

In a building programme the event that all the materials will be delivered at the correct time is M, and the event that the building programme will be completed on time is F. Given that $P\left(M\right)=0.8$ and $P(M\bigcap F)=0.65$. If $P\left(F\right)=0.7$, find the probability that the building programme will be completed on time if all the materials are not delivered at the correct time.

Answer 1

$P\left(F/M^{\prime }\right)=\frac{P(F\bigcap M^{\prime })}{P\left(M^{\prime }\right)}$
$=\frac{P\left(F\right)-P(F\bigcap M)}{(1-P\left(M\right))}$
$=\frac{0.7-0.65}{1-0.8}=\frac{0.05}{0.2}$
$=\frac{5}{20}=\frac{1}{4}$