CA Foundation · Quantitative Aptitude · Theoretical Distributions
A discrete random variable X takes the values 1, 2, 3 and 4 with probabilities k, 2k, 3k and 4k respectively. What is the value of P(X ≥ 3)?
P(X ≥ 3) is 0.7. The probabilities sum to 10k, which must equal 1, so k is 0.1. Then P(3) is 0.3 and P(4) is 0.4, and adding them gives 0.7. Using only P(X = 4) would wrongly give 0.4.
- A0.3
- B0.5
- C0.7Correct
- D0.4
Explanation
The probabilities must sum to 1, so k + 2k + 3k + 4k = 10k = 1 and k = 0.1. P(X ≥ 3) = P(3) + P(4) = 0.3 + 0.4 = 0.7. The value 0.4 is only P(X = 4), which ignores X = 3.
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