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# Probability Number cube

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What is the probability of rolling a number greater than 4 on a number cube and then spinning an even number on a spinner divided into 12 equal sectors numbered 1 through 12?

RedBlue  Dec 21, 2017
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#1
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Let's start from the top:

There is a 1/36 chance of rolling a 2

There is a 2/36 chance of rolling a 3

There is a 3/36 chance of rolling a 4

Adding them up, we get 6/36, or 1/6.

Subtracting this from unity (1) we get 5/6.

There is a 1/12 chance of spinning a 2

There is a 1/12 chance of spinning a 4

There is a 1/12 chance of spinning a 6

There is a 1/12 chance of spinning a 8

There is a 1/12 chance of spinning a 10

There is a 1/12 chance of spinning a 12

Adding them up, we get 6/12, or 1/2

Multiplying the numerators and denominators horizontally, we get \(\tfrac{5}{12}\).

Did this help? I hope it did!

helperid1839321  Dec 21, 2017
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That's wonderful, thank you.

RedBlue  Dec 21, 2017
#3
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Assuming that  the number cube has the possible outcomes of1,2,3,4,5 or 6.....the probability of rolling a number >  4     =  [  2 favorable outcomes ] / [6 possible outcomes ]  =  2/6  = 1/3

And the probability of spinning an even number =

[ 6 favorable outcomes] / [ 12 possible outcomes] =

6/12   =   1/2

So....the probability  =  P(first event) * P(second event)  =  (1/3) * (1/2)   =  1/6

CPhill  Dec 21, 2017

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