math 411 homework1

# math 411 homework1 - 1 2 Let A = “there is at most 1...

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Department of Mathematics Fall 2011 Volodymyr Nekrashevych Math 411 — Problem Set 1 Issued: 09.02 Due: 09.09 1.1. Two dice are rolled. What is the probability that (a) the two numbers will diﬀer by 1 or less and (b) the maximum of the two numbers will be 5 or larger? 1.2. Suppose Ω = { a,b,c } , P ( { a,b } ) = 0 . 7, and P ( { b,c } ) = 0 . 6. Compute the probabilities of { a } , { b } , and { c } . 1.3. Given two events A and B with P ( A ) = 0 . 4, and P ( B ) = 0 . 7, what are the maximum and minimum possible values for P ( A B )? 1.4. A family has 3 children, each of whom is a boy or a girl with probability
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Unformatted text preview: 1 / 2. Let A = “there is at most 1 girl” B = “the family has children of both sexes.” (a) Are A and B independent? (b) Are A and B independent if the family has 4 children? 1.5. Roll two dice. Let A = “the sum is even” and B = “the sum is divisible by 3,” that is B ∈ { 3 , 6 , 9 , 12 } . Are A and B independent? 1.6. Suppose we roll three tetrahedral dice that have 1, 2, 3, and 4 on their four sides. Find the distribution of the sum of the three numbers....
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