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# Casework Probability Problem

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If three, standard, 6-faced dice are rolled, what is the probability that the sum of the face up integers is 16?

Jul 27, 2022

### 5+0 Answers

#1
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The only possible combinations are

5 5 6

5 6 5

6 5 5

So the probability is 3/6^3 = 1/72.

Jul 27, 2022
#2
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What about the case where we get 4, 6, 6 :)

Jul 27, 2022
#3
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Did it say the dice are distinguishable? Do we have to consider that?

Jul 27, 2022
#4
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There are $$6^3 = 216$$ ways to roll the dice

There are only 2 ways to get 16:  $$(5, 5, 6)$$$$(4, 6, 6)$$

In both cases, there are $$3! \div 2! = 3$$ ways to order them

Thus, the probability is $${2 \times 3 \over 216} = {6 \over 216} = \color{brown}\boxed{1 \over 36}$$

Jul 27, 2022
#5
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Good method. I think that is correct. :)

Jul 27, 2022