# exercise26 - Exercise 26 Philosophy 102(Maher Spring 2009 1...

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Exercise 26 Philosophy 102 (Maher) Spring 2009 1. In the following questions, say which (if either) of H 1 and H 2 is favored by E . Justify your answers using either the deﬁnition of favoring or the law of likelihood. (a) p ( E | H 1 ) = 0 . 6, p ( E | H 2 ) = 0 . 7, p ( H 1 ) = 0 . 4, p ( H 2 ) = 0 . 6. (b) p ( H 1 | E ) = 0 . 5, p ( H 2 | E ) = 0 . 5, p ( H 1 ) = 0 . 6, p ( H 2 ) = 0 . 4. (c) p ( H 1 | E ) = 0 . 5, p ( H 2 | E ) = 0 . 4, p ( H 1 ) = 0 . 25, p ( H 2 ) = 0 . 2. (d) p ( E | H 1 ) = 0 . 5, p ( E | H 2 ) = 0 . 4, p ( H 1 ) = 0 . 25, p ( H 2 ) = 0 . 2. (e) An urn contains 100 dice, of which 99 are fair and 1 is biased so it lands six 20% of the time. A die is drawn randomly from the urn and tossed once. Let E = the die lands six, H 1 = it is the biased die, H 2 = it is one of the fair dice. (f) A card is drawn from a normal deck of 52 cards. Let E = the card is red, H 1 = it is a heart, H 2 = it is the 7 of diamonds. (g) A medical test has a false positive rate of 60% but no false negatives. Let
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