X and Y are two independent event. If (P(X) = frac{1}{5}) and (P(X cap Y) = frac{2}{15}), find (P(Y)).
-
A.
(frac{2}{3}) -
B.
(frac{2}{5}) -
C.
(frac{1}{3}) -
D.
(frac{1}{5})
Correct Answer: Option A
Explanation
For independent events (P(X cap Y) = P(X) times P(Y))
(frac{2}{15} = frac{1}{5} times P(Y))
(P(Y) = frac{2}{15} ÷ frac{1}{5} = frac{2}{3})