Casework Probability Problem

Question

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297

5

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

Guest Jul 27, 2022

Guest · Answer 1 · 2022-07-27T06:52:37

The only possible combinations are

5 5 6

5 6 5

6 5 5

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

Voldemort · Answer 2 · 2022-07-27T06:57:10

What about the case where we get 4, 6, 6 :)

Serakit · Answer 3 · 2022-07-27T06:57:54

Did it say the dice are distinguishable? Do we have to consider that?

BuilderBoi · Answer 4 · 2022-07-27T07:01:40

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 ${2 \times 3 \over 216} = {6 \over 216} = \color{brown}\boxed{1 \over 36}$

Serakit · Answer 5 · 2022-07-27T07:03:03

Good method. I think that is correct. :)