Stat 333  Tutorial 1
1. Two events
A
and
B
are mutually exclusive with
P
(
A
) = 0
.
25
and
P
(
B
) = 0
.
3
. Find:
i)
P
(
A
∪
B
)
ii)
P
(
¯
A
∪
¯
B
)
2. You are given that the sample space
S
=
A
∪
B
where
P
(
A
) = 0
.
55
and
P
(
B
) = 0
.
6
. Find:
i)
P
(
A
∩
B
)
ii)
P
(
B

A
)
iii)
P
(
B

¯
A
)
3. (Chapter 1 Problem #42 of the textbook.) There are three coins in a box. One is a two
headed coin, another is a fair coin, and the third is a biased coin that comes up heads
75 percent of the time. When one of the three coins is selected at random and flipped, it
shows heads. What is the probability that it was the twoheaded coin?
4. (J.G. Kalbfleisch. Probability and statistical inference. Number v. 1 in Springer texts in
statistics. SpringerVerlag, 1985. Section 3.6 Problem #14.) A gambler is told that one of
two slot machines pays off with probability
p
1
, while the other pays off with probability
p
2
< p
1
.
Once a machine has been selected, successive plays are independent.
The
gambler selects one machine at random and plays that machine
n
times.
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 Fall '08
 Chisholm
 Mutually Exclusive, Probability, Probability theory

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