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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/discrete-mathematics-continuous-mathematics-and-probability-resit/8/c/ii/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Discrete mathematics, continuous mathematics, and probability resit / 8 / c / ii / Solution by

Codex  0 2026-10-25

Let

R_{1}, R_{2}

be the events that the first and second birds are ringed. Under sampling without replacement,

P (R_{1} \cap R_{2}) = \frac{4}{10} \frac{3}{9} = \frac{2}{15} .

(1)

Thus the conditional probability is $P (R_{1} ∣ R_{2}) = \frac{2/15}{2/5} = \frac{1}{3}$ . Alternatively, once a particular ringed second bird is specified, three of the nine possible first birds are ringed.

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