Question

Two events $K$ and $L$ can cause delay in construction activity when occurring either each independently or both together, but the two events are not statistically independent of each other. The probability that at least one of the events occurs in 0.75 and the probability that each one occurs by itself is 0.45. The critical probability for occurrence of delay in the activity is

• A. $\frac{2\times 0.45-0.75}{0.45}$
• B. $\frac{0.75-0.45}{0.75}$
• C. $\frac{0.75}{0.45+0.75}$
• D. $\frac{2\times 0.45-0.75}{0.75}$

Answer 1

The correct option is A $\frac{2\times 0.45-0.75}{0.45}$

$P(K\cap L)=P\left(K\right)+P\left(L\right)-P(K\cup L)\therefore P(K\cap L)=2\times 0.45-0.75\text{Critical probability for delay in activity}\therefore P\left(K/K\right)=\frac{P(K\cap L)}{P\left(L\right)}=\frac{2\times 0.45-0.75}{0.45}$