A random variable X has the probability distribution X = x 1 2 3 4 5 6 7 8 P(X = x) 0.23 0.15 0.12 0.10 0.20 0.07 0.08 0.05 for the events E = X is a prime number and F = X 3 , then P (E F)=

Step-by-step solution

The event E is that X is a prime number. From the given values, the prime numbers are 2, 3, 5, 7 . E = 2, 3, 5, 7 The event F is that X 3 . From the given values, the numbers less than or equal to 3 are 1, 2, 3 . F = 1, 2, 3 The union of events E and F is: E F = 1, 2, 3, 5, 7 The probability P(E F) is the sum of the probabilities of these individual outcomes: P(E F) = P(X=1) + P(X=2) + P(X=3) + P(X=5) + P(X=7) Substituting the values from the probability distribution table: P(E F) = 0.23 + 0.15 + 0.12 + 0.20 + 0.08