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Meyer rolls two fair, ordinary dice with the numbers 1,2,3,4,5,6 on their sides. What is the probability that AT LEAST one of the dice shows a square number?

 Jan 18, 2018
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Meyer rolls two fair, ordinary dice with the numbers 1,2,3,4,5,6 on their sides. What is the probability that AT LEAST one of the dice shows a square number?

 

So one of the numbers must be 1 or 4

 

the posibilities are 

P(1,anything)  = (1/6)*1 =   1/6

P(4,anything) = 1/6

so

P(1, or 4 and any number on the other die) = 2/6

P(any number, 1 or 4) = 2/6

 

so together that is 4/6  trouble is some combinations have been added twice.

 

P(first die is 1 or 4, AND second die is 1 or 4) = 2/6 * 2/6 = 4/36 

 

So the prob that you want will  be  2/6  +  2/6  - 4/36 = 20/36 = 5/9

 

You can check it by counting them.  To get all the combinations just do it in a 6 by 6 grid.

 Jan 18, 2018

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