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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 Spring '08
 WEINBERG
 Philosophy, Randomness, Type I and type II errors, Dice, H1, H1 E

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