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Paco uses a spinner to select a number from 1 through 5, each with equal probability. Manu uses a different spinner to select a number from 1 through 10, each with equal probability. What is the probability that the product of Manu’s number and Paco’s number is less than 30? Express your answer as a common fraction.

 Nov 4, 2019
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There are (5+10) nCr 2 =105 outcomes and they are as follows:

 

(1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 14, 14, 15, 15, 15, 15, 16, 16, 16, 18, 18, 18, 18, 20, 20, 20, 20, 20, 20, 21, 21, 24, 24, 24, 24, 25, 27, 27, 28, 28, 30, 30, 30, 30, 32, 32, 35, 35, 36, 36, 40, 40, 40, 40, 42, 45, 45, 48, 50, 50, 54, 56, 60, 63, 70, 72, 80, 90) = 105 outcomes

 

There are 77 numbers < 30. Therefore, the probability is:

77 / 105 = 11 / 15

 Nov 4, 2019

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