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Problem 2.

MA 485-585 PROBABILITY THEORY HOMEWORK #2 Submission deadline: February 7. Each problem is 20 points 1. We flip a fair coin until we get the 3-rd Head. What is the probability that we get exactly 6 Tails? 2. We flip a loaded coin with P(H)-p (0 < p < 1) until we get the first Tail. Let N denote the (random) number of flips needed. We know that P(N What is p? 12 125 3) - 3. We have a standard deck of 52 French (Bridge) cards, from which we randomly select a hand of 5. What is the probability that we get a street, i.e. a sequence of 5 consecutive numbers/figures? (The suits are irrelevant. The streets are NOT cyclic, i.e. the A is not followed by 2.) 4. We know that P(nB0, P B 1/4, P(B2)-3/4, P(A) 1/8. What is the maximum possible value of the product P(AB) . PAB)? 5. Let B, B2, B3 be pairwise exclusive. P(B1-1/8. P(Ba)-1/4, PBs)-5/8, P(AIB. )-1. P(A1B2)-1/3. P(A1B3-1/3. Calculate P(B21A)

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