Question

If the probability of $X$ to fail in the examination is$0.3$ and that for $Y$ is $0.2$, then the probability that either $X$ or $Y$ fail in the examination is

• A. $0.5$
• B. $0.44$
• C. $0.6$
• D. $noneofthese$

Answer 1

The correct option is B

$0.44$

Explanation for correct option :

Find the the probability that either $X$ or $Y$ fail in the examination is :

The probability that $X$ fails in the exam $=0.3$

The probability that $Y$ fails in the exam $=0.2$

The probability that either $X$ or $Y$ fails in the exam, $P\left(XUY\right)$

We know that $P\left(XUY\right)=P\left(X\right)+P\left(Y\right)-P(X\cap Y)$

As, $X$ and $Y$ are independent events, then,$P(X\cap Y)=P\left(X\right).P\left(Y\right)$

$$\begin{gathered} \therefore P\left(XUY\right)=P\left(X\right)+P\left(Y\right)-P(X\cap Y) \\ \Rightarrow P\left(XUY\right)=0.3+0.2–(0.3)(0.2) \\ \Rightarrow P\left(XUY\right)=0.5–0.06 \\ \Rightarrow P\left(XUY\right)=0.44. \end{gathered}$$

Hence option (B) is correct.