Finite Math Problem?

Question

What is the probability that exactly one die shows a 5 given that the sum of the numbers is 11?
-The two dice are fair

Answer 1

The only possibility to get 11 with two dice is to get one 6 and one 5.
There is a 100% chance you have exactly one 5 if the sum of the two dice is 11.

Answer 2

Hi,
The key phrase here is "given that the sum of the numbers is 11."
In that case you have a conditional probability for which you can have only two situtions:
Die #1...Die #2
....5..........6
....6..........5
In either case, you have one and only one 5, so the probability of getting a 5 is 100%.
You can work it out with conditional probability, but it's a little more abstract than this simple reasoning process.

FE

Answer 3

If you throw two fair dice, the only possible outcomes that include a 5 are

5,1
5,2
5,3
5,4
5,5
5,6
1,5
2,5
3,5
4,5
5,5
and
6,5

which is 12 possible outcomes of which only 2 give the sum of 11....so the odds are 2/12, or 1/6 (or 0.1666)

Answer 4

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