# HW1 - Section 2.1-2.2 Sample space(p.38 2.4(a An experiment...

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Section 2.1-2.2 Sample space (p.38) 2.4 (a) An experiment involves tossing a pair of dice, 1 green and 1 red, and recording the numbers that come up. If x equals the outcome on the green die and y the outcome on the red die, describe the sample space S by listing the elements ( x, y ). sol) S = { (1 , 1) , (1 , 2) , (1 , 3) , (1 , 4) , (1 , 5) , (1 , 6) , (2 , 1) , (2 , 2) , (2 , 3) , (2 , 4) , (2 , 5) , (2 , 6) , (3 , 1) , (3 , 2) , (3 , 3) , (3 , 4) , (3 , 5) , (3 , 6) , (4 , 1) , (4 , 2) , (4 , 3) , (4 , 4) , (4 , 5) , (4 , 6) , (5 , 1) , (5 , 2) , (5 , 3) , (5 , 4) , (5 , 5) , (5 , 6) , (6 , 1) , (6 , 2) , (6 , 3) , (6 , 4) , (6 , 5) , (6 , 6) } 2.5 An experiment consists of tossing a die and then flipping a coin once if the number on the die is even. If the number on the die is odd, the coin is flipped twice. Using the notation 4 H , for example, to denote the outcome that the die comes up 4 and then the coin comes up heads, and 3 HT to denote the outcome that the die comes up 3 followed by a head and then a tail on the coin, construct a tree diagram to show the 18 elements of the sample space S . sol) S = { 1 HH, 1 HT, 1 TH, 1 TT, 2 H, 2 T, 3 HH, 3 HT, 3 TH, 3 TT, 4 H, 4 T, 5 HH, 5 HT, 5 TH, 5 TT, 6 H, 6 T } 1

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2.14 If S = { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } and A = { 0 , 2 , 4 , 6 , 8 } , B = { 1
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