 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-2/7/solution

The implication means that

A \subseteq B

, so

A \cap B = A

P (A ∣ B) = \frac{P ( A \cap B )}{P ( B )} = \frac{1/3}{1/2} = \frac{2}{3} .

This implication gives

P (B ∣ A) = 1

; it does not make the two events independent.

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