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Unformatted text preview: coin 2 coin
head 3 coin 3 coin
head 4 coin 4 coin
head 5 coin 4 coin 2
0 0.2 0.25 0.2 0.5 0.2 0.75 0.2 1 0.2 2
(b) According to the total probability theorem, 5 0.5 1 2 heads 2 heads1 coin 1 coin
2 heads 2 coin 2 coin
2 heads 3 coin 3 coin
2 heads 4 coin 4 coin
2 heads 5 coin 4 coin 2
0 0.2 0.25
0.2 0.5
0.2 0.75
0.2 1
0.2 2
0.375 1 (c) Given we got a head, according to the Bayes’ rule,
4 coinhead 1 head 4 coin 4 coin
2
head 0.15
1.5
0.5 0.3 0.5 ; (d) Given we got a head at the 1st toss, according to the Bayes’ rule,
get a head at the 2 tossget a head at the 1 toss 1
.
. 1 2 0.75 1 . As can be seen, the confidence of getting a head at the second toss is higher if we get a head at the first toss. 6...
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 Fall '14

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