Question

If P(F) = 0.35 and P(E∪F) = 0.85 and E and F are independent events. Find P(E).

Answer 1

Given: P(F) = 0.35 and P(E∪F) = 0.85

To find: P(E)

Solution:

• Now we have given that E and F are independent events.

• Also we have given that P(F) = 0.35 and P(E∪F) = 0.85

• Now we have:

                 P(E∪F) = P(E) + P(F) - P(E∩F)

                 P(E∪F) = P(E) + P(F) - (P(E) x P(F))

• Now putting the values in formula, we get:

                 0.85 = P(E) + 0.35 - (0.35)P(E)

                 0.50 = 0.65 x P(E)

                 P(E) = 0.50 / 0.65

                 P(E) = 50 / 65

                 P(E) = 10 / 13

Answer:

                  So the value of P(E) =  10 / 13