Question

If the probabilities for $A$ to fail in an examination is $0.2$ and that for $B$ is $0.3$, then the probability that either $A$ or $B$ fails is

• A. $\le 0.5$
• B. $0$
• C. $0.5$
• D. $>0.5$

Answer 1

The correct option is A $\le 0.5$

It is given that

$P\left(A^{\prime }sfailure\right)=0.2$

and $P\left(B\text{'}sfailure\right)=0.3$

We know, for any two events $X$ and $Y$

$P(X\cup Y)\le P\left(X\right)+P\left(Y\right)$

$\therefore P\left[\right(A^{\prime }sfailure)\cup (B^{\prime }sfailure\left)\right]\le P\left(A^{\prime }sfailure\right)+P\left(B^{\prime }sfailure\right)$

$\Rightarrow P\left(AorBfails\right)\le P\left(A^{\prime }sfailure\right)+P\left(B^{\prime }sfailure\right)$

$\Rightarrow P\left(AorBfails\right)\le 0.2+0.3$

$\Rightarrow P\left(AorBfails\right)\le 0.5$

Final Answer: C