PHL246H1 Lecture Notes - T Helper Cell
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Pr(a is not white|b) < pr(a is a swan|b). Suppose further that, given your background assumptions b, your degree of belief that all swans are white is independent of a not being white as well as of a being a swan: Pr(a is not white|all swans are white, and b) = pr(a is not white|b) Pr(a is swan|all swans are white, and b) = pr(a is a swan white|b) Show that these three assumptions imply that conditioning on the information that a is a white swan increases your degree of belief in the swan-hypothesis. Pr(all swans are white|a is a white swan, and b) > pr(all swans are white|b) (2 points) There are four possible outcomes: hh, ht, th, and tt. Hypothesis fair says that the coin is fair, i. e. that the chance of heads equals the chance of tails and that the two coin tosses are independent and identically distributed.
