JEE MAIN - Mathematics (2022 - 24th June Evening Shift - No. 11)
A random variable X has the following probability distribution :
| X | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| P(X) | k | 2k | 4k | 6k | 8k |
The value of P(1 < X < 4 | X $$\le$$ 2) is equal to :
$${4 \over 7}$$
$${2 \over 3}$$
$${3 \over 7}$$
$${4 \over 5}$$
Explanation
$$\because$$ x is a random variable
$$\therefore$$ $$k + 2k + 4k + 6k + 8k = 1$$
$$\therefore$$ $$k = {1 \over {21}}$$
Now, $$P(1 < x < 4\,|\,x \le 2) = {{4k} \over {7k}} = {4 \over 7}$$
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