Name______________________________________________ Date ______________ Period ___________ Discrete Math Chapter 7 Final Exam Review Find the number of subsets of the set. 7) A lottery game has balls numbered 0 through 1) {1, 2, 3, . . . , 7} 9. A randomly selected ball has an even number or a 5. A) 124 B) 256 C) 16 D) 128 3 2 A) 5 B) 2 C) D) 5 5 Insert "⊆" or "⊈" in the blank to make the statement true. 2) {h, j, e} {h, j, e} A) ⊈ B) ⊆
Find the probability of the indicated event. 8) Each digit from the number 9,626,446 is written on one of seven cards. The digit 9, 6, or 2 is written on a randomly drawn card. 9 3 5 2 A) B) C) D) 7 7 7 7
Let U = {q, r, s, t, u, v, w, x, y, z}; A = {q, s, u, w, y}; B = {q, s, y, z}; and C = {v, w, x, y, z}. List the members of the indicated set, using set braces. 3) C' ∩ A' A) {r, t} B) {q, s, u, v, w, x, y, z} C) {q, r, s, t, u, v, x, z} D) {w, y}
Suppose P(C) = .048, P(M ∩ C) = .044, and P(M ∪ C) = .524. Find the indicated probability. 9) P(M' ∪ C') A) .004 B) .466 C) .956 D) .524
Use a Venn Diagram and the given information to determine the number of elements in the indicated set. 4) n(U) = 87, n(A) = 40, n(B) = 40, n(C) = 22, n(A ∩ B) = 6, n(A ∩ C) = 6, n(B ∩ C) = 8, and n(A ∩ (B ∩ C)) = 3. Find n(((A ∪ B) ∪ C)'). A) 33 B) 31 C) 2 D) 3
Solve the problem. 10) If two cards are drawn without replacement from an ordinary deck, find the probability that the second card is a face card, given that the first card was a queen. 4 3 A) B) 17 13
Use a Venn diagram to answer the question. 5) A survey of 122 college students was done to find out what elective courses they were taking. Let A = the set of those taking art; B = the set of those taking basket weaving; and C = the set of those taking canoeing. The study revealed the following information: n(A) = 45; n(B) = 55; n(C) = 40; n(A ∩ B) = 12; n(A ∩ C) = 15; n(B ∩ C) = 23; n(A ∩ B ∩ C) = 2. How many students were not taking any of these electives? A) 10 B) 32 C) 40 D) 30
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Find the probability. 11) A family has five children. The probability of having a girl is 1/2. What is the probability of having at least 4 girls? Round the answer to the fourth decimal place. A) .0313 B) .1563 C) .3125 D) .1875 Solve the problem. Express the answer as a percentage. 12) 34% of the workers at Motor Works are female, while 70% of the workers at City Bank are female. If one of these companies is selected at random (assume a 50 -50 chance for each), and then a worker is selected at random, what is the probability that the worker will be female? A) 52% B) 70% C) 36% D) 34%
Find the probability of the given event. 6) A card drawn from a well-shuffled deck of 52 cards is a red ace. 1 1 A) B) 13 52 C)
11 51
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