Stat 126
Exam 1
Spring 2006
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(1) Assume that events
A
and
B
are independent, events
A
and
C
are mutually exclusive,
and events
B
and
C
are also mutually exclusive. Moreover,
P
(
A
) = 1
/
2,
P
(
B
) = 1
/
3, and
P
(
C
) = 1
/
4.
Hint: Parts (a), (b) and (c) would help each other.
(a) Draw a Venn diagram.
(b) Calculate
P
(
A
∩
B
c
∩
C
c
).
(c) Calculate
P
(
A
∪
B
∪
C
).
(d) Calculate
P
(
B
or
C

A
).
1
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View Full Document(2) Jeﬀ plays the following game. A fair die is rolled. If the number on the die is odd, then
Jeﬀ loses. If the number on the die is even, the die is rolled again. In that case Jeﬀ wins if the
second number matches the ﬁrst and loses otherwise.
(a) Construct a tree diagram.
(b) Find the probability that Jeﬀ wins.
(c) Given that Jeﬀ loses, what is the conditional probability that he loses after the die is rolled
twice?
(3) Imagine that Detroit Pistons will play Dallas Mavericks in the next NBA Finals. The team
that reaches 4 wins ﬁrst will be the champion. Hence the series may ﬁnish in at least 4 games
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 Fall '08
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 Probability, pistons, Strike price

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