If P(B) = 2P(A|B) = 0.4, then find P(AnB).

1.	If P(B) = 2P(A\|B) = 0.4, then find P(AnB).
Answer» P(B) = 2P(A\|B) = 0.4 ∴ P(B) = 0.4, 2P(A\|B) = 0.4 ∴ P(A\|B) = \(\frac{0.4}{2}\) = 0.2 Now, P(A\|B) = \(\frac{P(A∩B)}{P(B)}\) ∴ P(A ∩ B) = P(A\|B) ∙P(B) = 0.2 × 0.4 = 0.08

Answer»

P(B) = 2P(A|B) = 0.4

∴ P(B) = 0.4, 2P(A|B) = 0.4

∴ P(A|B) = \(\frac{0.4}{2}\) = 0.2

Now, P(A|B) = \(\frac{P(A∩B)}{P(B)}\)

∴ P(A ∩ B) = P(A|B) ∙P(B)

= 0.2 × 0.4 = 0.08

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If P(B) = 2P(A|B) = 0.4, then find P(AnB).

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