HW3 - IE 111 Fall 2007 Homework #3 Due Beginning of Class...

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IE 111 Fall 2007 Homework #3 Due Beginning of Class on Monday 9/24 Question 1 Suppose we have a biased coin such that P(head) P(tail). Suppose I flip the coin three times. Let the random variable X be the number of heads in the 3 flips. You are given the following information: P(X=0) = 1/27 P(X=1) = 6/27 P(X=2) = ? P(X=3) = 8/27 a) Find P(X=2) b) Find P( 1 X < 2) c) Find P( X=1 | X 1) Question 2 Three fair coins are tossed. Find the following: a) P(TTH) b) P(more heads than tails) c) P(more heads than tails | at least one tail) d) P(Exactly one head | at least two tails Question 3 Suppose that P(A|B) = 0.3 and P(B) = 0.5. Find: a) P(A and B) b) P(A and B) Question 4 Three events A, B, and C are independent with the following probabilities: P(A)=0.6 P(B)=0.4 P(C)=0.2 a) What is the probability that at least one of the three events occurs? b) Find P(A|C) c) Find the probability that exactly two of the events occur.
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Question 5 If P(A|B)=0.4, P(B)=0.8, and P(A)=0.4, are events B and A independent? Prove it. Question 6 I have 2 identical six sided dice. The dice are fair in that each of the six sides is equally likely to come up. The only difference between these dice and regular dice is that three sides are labeled "1", two sides are labeled "2" and one side is labeled "3" (this is true for
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HW3 - IE 111 Fall 2007 Homework #3 Due Beginning of Class...

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