HW2-sol (Math 425)

HW2-sol (Math 425) - Math 425 – Section 008 Homework 2...

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Unformatted text preview: Math 425 – Section 008 Homework 2 – Ch. 2, problems 3, 8, 13(a), 15(d), 32, 33, 37, 45, 47 Problem 3. Two dice are thrown. Let E be the event that the sum of the dice is odd; let F be the event that at least one of the dice lands on 1; let G be the event that the sum is 5. Describe the events EF,E ∪ F,FG,EF c ,EFG . Solution. Notice that there are various ways to describe the same events. For instance, EF can be described as the event that one of the dice lands 1 while the other is even. FG is the event that one of the dice lands on 1 while the other lands on 4. The event EFG is the same as FG , because E ⊃ G . EF c is the event that the sum is odd and no die lands on 1. The event E ∪ F just says the following: if the sum is even, then there must be at least one die that lands on 1. Problem 8. Suppose that A and B are mutually exclusive events for which P ( A ) = 0 . 3 and P ( B ) = 0 . 5. What is the probability that (a) either A or B occurs; (b) A occurs but B does not; (c) both A and B occur; Solution. (a) Since AB = ∅ , we have P ( A ∪ B ) = P ( A ) + P ( B ) = 0 . 8. (b) Since A and B are mutually exclusive, AB c and A are in fact the same event. So, P ( AB c ) = P ( A ) = 0 . 3. (c) P ( AB ) = P ( ∅ ) = 0 . Problem 15. If it is assumed that all ( 52 5 ) poker hands are equally likely, what is the conditional probability of being dealt (d) three of a kind? (The cards have denominations(d) three of a kind?...
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HW2-sol (Math 425) - Math 425 – Section 008 Homework 2...

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