Question

If the probability of $A$ to fail in an examination is $0.2$ and that for $B$ is $0.3$, then the probability that either $A$ or $B$ fail is $0.5$. If this is true enter $1$, else enter $0$.

Answer 1

Since $A$ and $B$ are independent events, we have $P(A\cup B)=P\left(A\right)P\left(B\right)$ $\therefore P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$ $=P\left(A\right)+P\left(B\right)-P\left(A\right)P\left(B\right)$ $=0.2+0.3-0.2\times 0.3$ $=0.50-0.06=0.44$