In Discrete Mathematics!!!!!!!!!!!!!!!!! 3. Given a set X and subsets A and B of X find A x B, A U B, AB, A-B, B-A, Aº, Bc.a.) X={1,2,3,4,5,6,7,8,9,10),A={1,3,5,7,9), B={1,2,8,9}.b.) X={1,2,3,..., 14, 15), A={5,9,13}, B={3,7,11,15}.

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Answered: 3. Given a set X and subsets A and B of…

3. Given a set X and subsets A and B of X find A x B, A U B, AB, A-B, B-A, A, Bc. a.) X={1,2,3,4,5,6,7,8,9,10), A={1,3,5,7,9), B={1,2,8,9}. b.) X={1,2,3,..., 14, 15), A={5,9,13), B=(3,7,11,15}.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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(a) Find the probability of being dealt an "aces over kings" full house (three aces and two kings). (Round your answer to six decimal places.)(b) Find the number of different types of full houses. (Ignoring suit.)ways(c) Find the probability of being dealt a full house. (Round your answer to six decimal places.)
Discrete mathematics ( probability )
Problem 1. Suppose you roll a fair 20-sided die. Are the following events independent? (a) E₁ is the event that the result of the die roll is even. E2 is the event that the result of the die roll is less than or equal to 6. (b) E₁ is the event that the result of the die roll is even. E2 is the event that the result of the die roll is divisible by 4. (c) E₁ is the event that the result of the die roll is divisible by 4. E₂ is the event that the result of the die roll is divisible by 6. (d) E₁ is the event that the result of the die roll is divisible by 4. E2 is the event that the result of the die roll is divisible by 5.
Example 1. Let a coin be tossed 5 times; what is the probability of exactly 3 heads out of the 5 tosses? We can represent any sequence of 5 tosses by a symbol such as thhth. The probability of this particular sequence (or any other particular sequence) is )5 since the tosses are independent (see Example 1 of Section 3). The number of such sequences containing 3 heads and 2 tails is the number of ways we can select 3 positions out of 5 for heads (or 2 for tails), namely C(5, 3). Hence, the probability of exactly 3 heads in 5 tosses of a coin is C(5, 3)(÷)5. Suppose a coin is tossed repeatedly, say n times; let r be the number of heads in the n tosses. We want to find the probability density function p = f(x) which gives the probability of exactly x heads in n tosses. By generalizing the case of 3 heads in 5 tosses, we see that (7.1) f (1) = C(n, æ)(})"
Rework problem 26 from the chapter 3 review section of your text, involving the rolling of two fair dice. Answer the following questions. (1) What is the probability that the sum is 11, given that at least one of the numbers rolled is even? (2) What is the probability that at least one number is even, given that the sum is 11? (3) What is the probability that at least one number is even, given that the sum is 10?
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Please answer (a), (b), and (c).