Explanation Given Information: Two dice, one green and one red are rolled and losing combinations are doubles and outcomes in which red die shows an even number, the green die shows an odd number and other combinations are the winning ones. Formula used: The union of two sets A and B is given by the set of all elements that are either in A or in B (or in both). A ∪ B = { x | x ∈ A or x ∈ B } For events E and F , n ( E ∪ F ) = n ( E ) + n ( F ) − n ( E ∩ F ) . The formula for cardinality rule is n ( C ′ ) = n ( S ) − n ( C ) , where C is any set. Calculation: Consider the given information. Since, each die has 6 number of outcomes. Thus, the set of outcomes when two dice, one red and one green are rolled is 6 × 6 = 36 . Let S the set of outcomes when two dice, one red and one green are rolled be the sample space . Thus, n ( S ) = 36 . Let A be the set of doubles and B be the set of outcomes in which the green die shows an odd number and red die shows an even number. Since, there are 6 doubles, ( 1 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) , ( 4 , 4 ) , ( 5 , 5 ) , and ( 6 , 6 ) . Thus, n ( A ) = 6 . Since, there are 3 even and 3 odd numbers in a die, the number of outcomes in the set in which the green die shows an odd number and red die shows an even number is 3 × 3 = 9 . Thus, n ( B ) = 9 . Consider, the set of loosing combinations is the set of outcomes either in A or in B . Recall that the union of two sets A and B is given by the set of all elements that are either in A or in B (or in both). A ∪ B = { x | x ∈ A or x ∈ B } Thus, the set of losing combinations is the set A ∪ B . Consider, the set A ∩ B is the set of outcomes common to both A and B . Since, there is no outcome common in the sets A and B . Thus, A ∩ B = ∅ . Thus, n ( A ∩ B ) = 0 . Recall that for events E and F , n ( E ∪ F ) = n ( E ) + n ( F ) − n ( E ∩ F )

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ISBN: 9781337604956

Author: Waner

Publisher: CENGAGE L

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Chapter 6, Problem 13RE

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To calculate: The formula for cardinality rule and calculate the number of winning combinations where two dice, one green and one red are rolled and losing combinations are doubles and outcomes in which red die shows an even number, the green die shows an odd number and other combinations are the winning ones.

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Bundle: Finite Mathematics, 7th + WebAssign Printed Access Card for Waner/Costenoble's Finite Mathematics, 7th Edition, Single-Term

Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

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The formula for cardinality rule and calculate the number of winning combinations where two dice, one green and one red are rolled and losing combinations are doubles and outcomes in which red die shows an even number, the green die shows an odd number and other combinations are the winning ones.

Solution Summary: The author calculates the formula for cardinality rule and calculate the number of winning combinations where two dice, one green and one red are rolled and losing combinations are doubles.

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