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A discrete random variable X is distributed as follows: X: 1 2 3 4 5 6 7 8 P(X): 0.15 0.23 0.12 0.10 0.20 0.08 0.07 0.05 If E denotes the event that X is a prime number and F denotes the event that X < 4, then the value of P(E ∪ F) is

1. 0.50
2. 0.77
3. 0.35
4. 0.87

Correct answer: 0.35

Solution

The correct option is right because P(E ∪ F) is calculated by adding the probabilities of the events E and F, and then subtracting the probability of their intersection to avoid double counting. In this case, the prime numbers less than 4 are 2 and 3, and the total probability for event E (prime numbers) and event F (numbers less than 4) leads to a combined probability of 0.35.

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