Practice_Problems_Midterm1

Similarly prb wins 12 x pq 0 x p1q 1 x 1pq

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Unformatted text preview: 0. q = Pr(B scores) = 1/2 Pr(A wins) = Pr(A wins | A scores, B scores) x Pr(A scores, B scores)+ Pr(A wins | A scores, B doesn't score) x Pr(A scores, B doesn't score) + Pr(A wins | B scores, A doesn't score) x Pr(B scores, A doesn't score) + Pr(A wins | Neither A or B score ) x Pr(Neither A or B score). = 1/2 x pq + 1 x p(1 ­q) + 0 x (1 ­p)q + 1/2 x (1 ­p)(1 ­q) = 139/240. c) Since there is a possibility of draw, let E = A wins F = B wins. Answer = Pr(E occurs before F) Pr(A wins) = Pr(A wins | A scores, B scores) x Pr(A scores, B scores)+ Pr(A wins | A scores, B doesn't score) x Pr(A scores, B doesn't score) + Pr(A wins | B scores, A doesn't score) x Pr(B scores, A doesn't score) +...
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