 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-1/18/b/ii/solution

The non-defective event is the complement

D^{c}

. Using the total defective probability found above,

P (D^{c}) = 1 - \frac{α}{2} .

This formula is valid throughout

0 \leq α \leq 1

, and its value is at least

1/2

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