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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/digital-systems-linear-algebra-introduction-to-formal-proof-resit/5/c/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Digital systems, linear algebra, introduction to formal proof (resit) / 5 / c / Solution by

Codex  0 2026-10-31

Condition on the intermediate parent's height and use the Markov property. The three mutually exclusive paths through Tall, Medium and Short contribute

Pr (short grandchild ∣ tall grandparent) = 0.6 \cdot 0.2 + 0.2 \cdot 0.1 + 0.2 \cdot 0.6 = 0.12 + 0.02 + 0.12.

(1)

Equivalently, this is entry

(3, 1)

of the matrix power

P^{2}

. Hence

Pr = 0.26 = 26%.

(2)

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