MACM 201 Lecture 2: 201sol1
17 Sep 2017
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A1. (wp, ce) the probability that a tossed coin lands heads is p. when the coin is tossed twice, it is equally likely that both tosses are the same and that the tosses are not both tails. Pr(both tosses same) = pr(hh) + pr(t t ) Pr(tosses are not both tails) = 1 pr(t t ) These probabilities are equal when p2 + (1 p)2 = 1 (1 p)2, which rearranges to 3p2 4p + 1 = 0 and then factors as (3p 1)(p 1) = 0. The solutions are p = 1/3 and p = 1. The solution p = 1/3 is plausible for a physical (weighted) coin, but the solution p = 1 is not plausible because such a coin would always land heads. A2. (i) (cd) de ne the conditional probability pr(a | b), and derive an expression for it involving pr(b | a) but not pr(b).
