Question

Let A, B be events, with P(A) =.2, P(B) = .4, and P(A|B) = .25. Find P(A and B)

Answer 1

`p(a \: \cup \: b) = p(a) + p(b) - p(a \: \cap \: b) \\ p(a \: \cup \: b) = 0.2 + 0.4 - p(a \: \cap \: b) \\ p(a \: \cup \: b) = 0.6 - p(a \: \cap \: b) \\`

`but \: \: p(a \: \cap \: b) = p(a /b) * p(b) \\ p(a \: \cap \: b) = 0.25 * 0.4 = 0.1`

`p(a \: \cup \: b) = 0.6 - p(a \: \cap \: b) \\ p(a \: \cup \: b) = 0.6 - 0.1 \\p(a \: \cup \: b) = 0.5`