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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 ≤ 2) is equal to
- 4/7
- 2/3
- 3/7
- 4/5
Correct answer: 4/7
Solution
To find P(1 < X < 4 | x ≤ 2), we first calculate the probabilities of X being 1, 2, and 3, and then use the conditional probability formula. The total probability for x ≤ 2 is 7k, and the probability for 1 < X < 4 (which includes X = 2 and X = 3) is 10k. Thus, the conditional probability simplifies to 10k / 7k = 4/7.
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