Let E and F be two independent events. The probability that exactly one of them occurs is 11/25 and the probability of none of them occurring is 2/25. If P(T) denotes the probability of occurrence of the event T, then P(E) = ?, P(F) = ?

Given, P(E ∩ F') or P(F ∩ E') = 11/25 ⇒ P(E)P(F') + P(F)P(E') = 11/25
Let P(E) = x, P(F) = y ⇒ x(1 - y) + y(1 - x) = 11/25. (1)
P(E' ∩ F') = 2/25 ⇒ P(E')P(F') = 2/25 or (1 - x)(1 - y) = 2/25. (2)
Solving (1) and (2), we get
x = 3/5, y = 4/5 or x = 4/5, y = 3/5
P(E) = 3/5, P(F) = 4/5 or P(E) = 4/5, P(F) = 3/5