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What is the probability that the product of 3 single digit numbers is a multiple of 3.

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timw996 | Student, Grade 10

Posted September 14, 2013 at 3:11 PM via web

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What is the probability that the product of 3 single digit numbers is a multiple of 3.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 14, 2013 at 3:18 PM (Answer #1)

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A single digit number can be 0,1,2, 3, 4, 5, 6, 7, 8 or 9. Of these 3, 6 and 9 are multiples of 3.

The product of 3 numbers is a multiple of 3 if either of the three is a multiple of 3.

There are 10*10*10 = 1000 results of the multiplication of 3 single digit numbers. All of these are not unique, but that does not make a difference here. There are 3*10*10 = 300 results that are a multiple of 3.

This gives a probability of 0.3 that the product of 3 single digit numbers is a multiple of 3

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