GATE 2020 EC – Question 64
$X$ is a random variable with uniform probability density function in the interval $[-2,10]$. For $Y=2X-6$, the conditional probability $P(Y\le7\,|\,X\ge5)$ (rounded off to three decimal places) is ________.
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Correct answer: 0.29 to 0.31
Explanation
$Y\le7$ means $2X-6\le7$, i.e. $X\le6.5$. So $P(Y\le7\,|\,X\ge5)=\frac{P(5\le X\le6.5)}{P(X\ge5)}=\frac{1.5}{5}=0.3$.