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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: 0.77

Solution

Primes are {2,3,5,7}, X<4 is {1,2,3}, so E∪F={1,2,3,5,7}. P=0.15+0.23+0.12+0.20+0.07=0.77.

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