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Previous Year Question (PYQs)

In a tuition batch of two students, the probability that $X$ will pass the exam is $\frac{2}{5}$ and that of $Y$ is $\frac{3}{4}$. What is the probability that neither of $X$ and $Y$ will pass the exam? Assume that the outcomes of exams for $X$ and $Y$ are independent of each other.




Solution

Given,
$P(X\text{ passes})=\frac{2}{5}$

So,
$P(X\text{ does not pass})=1-\frac{2}{5}=\frac{3}{5}$

Also,
$P(Y\text{ passes})=\frac{3}{4}$

So,
$P(Y\text{ does not pass})=1-\frac{3}{4}=\frac{1}{4}$

Since both events are independent,

$P(\text{neither }X\text{ nor }Y\text{ passes})=\frac{3}{5}\times \frac{1}{4}$

$=\frac{3}{20}$


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