Conditional Probability & Independence

Question

Let E and F be events with P(E) = .4, P(F) = .8, and P(E | F) = .375. What is P(E ∩ F) ?

Answer 1

P(E and F) = P(E|F)/P(F) = 0.375/0.8 = 0.46875

Answer 2

Given: P(E) = .4, P(F) = .8, and P(E | F) = .375.

To Find: P(E ∩ F).

Solution: P(E | F) = P(E ∩ F) / P(F) [ Conditional probability ] .

0.375 = P(E ∩ F) / 0.8

P(E ∩ F) = 0.375 * 0.8

P(E ∩ F) = 0.3

Hope this helps!