 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-2/11/e/solution

The numerator event is contained in the conditioning event. The definition of conditional probability therefore gives

P (1 < X < 3 ∣ 1 < X < 6) = \frac{P ( 1 < X < 3 )}{P ( 1 < X < 6 )} = \frac{1 - 3 ^{- α}}{1 - 6 ^{- α}} .

The denominator is positive for all

α > 0

, and endpoint strictness is irrelevant for a continuous probability distribution.

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