Practice Exam:
1. You toss three fair dice. What is the probability that the three dice do not all three show the
same number?
Solved in class
2. Suppose that 30% of all houses need a paint job. Also, 15% of all houses need both a paint job
and a new roof. Further, 7% of all houses that need a new roof also need new windows.
Assume
that 50% of all houses that do not need a new paint job do need a new roof. What is the
probability that a randomly selected house needs a new roof?
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3.
Of the patients of a hospital, 30% of the redheads have had skin cancer, and 20% of the non
redheads have had skin cancer. Also, 40% of the patients are redheads.
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(a). What is the probability that a random patient there has had skin cancer?
(b). Patient Joe has cancer; what is the probability that he is a redhead?
4. Two of the cards of an ordinary deck of 52 cards are lost. What is the probability that a
random card drawn from this (defective) deck is a spade?
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5. I tell you that, for two events A and B, P(A) = 4/5, P(B  A) = 1/2, and that A and B are NOT
independent. (They are dependent.) For each statement, say “True”, “False”, or “Can't Tell”.
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 Spring '08
 Tucker,A
 Probability, Randomness, Dice, Handedness

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