## Idealist Group Title When rolling two dice, what is the probability that the sum is 7 given that one die is a 5? one year ago one year ago

1. geoffb Group Title

If one die is 5, there's only one possible result on the other die to get 7. What is the probability of rolling what you need?

2. DarkendSinz30 Group Title

There are 6 x 6 or 36 options, all are equally likely, 7 occurs 6 times, so the chances are 6/36 or 1/6. hope this helps?

3. Idealist Group Title

I don't get it. What do you mean by 7 occurs 6 times?

4. dpaInc Group Title

to get a 7: dice1 dice2 1 6 2 5 3 4 4 3 5 2 6 1 six different ways.. now how many of those have a 5 showing?

5. satellite73 Group Title

if you know that one die is a 5 then your sample space has only 6 elements in it of those six elements, exactly one gives a total of 7, namely (5,2)

6. satellite73 Group Title

therefore your answer is $$\frac{1}{6}$$

7. sirm3d Group Title

there are 11 outcomes when one of the outcome is 5.

8. satellite73 Group Title

@dpaInc is conditioning the other way that is, showing how to compute the probability that one die shows 5 given the total is 7

9. dpaInc Group Title

10. sirm3d Group Title

(1,5), (2, 5), (3,5), (4,5), (5,5), (5,6), (5,1), (5,2), (5,3), (5,4), (6,5)

11. sirm3d Group Title

there are only of those 11 outcomes that have a sum 7. so the probability is 2/11

12. sirm3d Group Title

there are only 2 of those 11 outcomes that have a sum 7. so the probability is 2/11

13. Idealist Group Title

You guys are so helpful, thank you!

14. sirm3d Group Title

thanks for the medal, @DarkendSinz30

15. Idealist Group Title

You're welcome.