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m1-06

# m1-06 - Stat 126 Exam 1 Spring 2006 Name ID I pledge that I...

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Stat 126 Exam 1 Spring 2006 Name: ID#: I pledge that I have neither given nor received unauthorized aid on this exam. Signature: (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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(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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m1-06 - Stat 126 Exam 1 Spring 2006 Name ID I pledge that I...

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