Unformatted text preview: 5
0.25 0.15 1 ; 0.6 1 , 0.5 0.5 , 2
so VAR 0
11
otherwise 1 0.1 1 0.4 0.4 1
0.5 is an arbitrarily small positive 1 0.5 . 4. [20 Marks] (a)
(b)
(c)
(d) There’re 5 different unfair coins and they all look the same. If we toss these 5 coins, the
probabilities of getting a head are
head
0,
head
0.25 ,
head
0.5 ,
head
0.75 and
head
1, respectively. Now we choose a coin randomly (equally
probable). Find out the probabilities of the following events:
[5’] We toss the coin and get a head;
[5’] We toss the coin twice and get two heads;
[5’] The coin we toss is the 4th coin given we get a head;
[5’] We toss the coin twice, and get a head at the second toss given we already get a head at
the first toss. Solution:
(a) According to the total probability theorem,
head
head1 coin 1 coin
head 2...
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 Fall '14
 Probability theory, $10, $50, $60, 2kg, 5kg

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