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## Idealist 2 years ago When rolling two dice, what is the probability that the sum is 7 given that one die is a 5?

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1. geoffb

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

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

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

4. dpaInc

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

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

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

7. sirm3d

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

8. satellite73

@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

yep ur right... my bad....

10. sirm3d

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

11. sirm3d

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

12. sirm3d

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

13. Idealist

You guys are so helpful, thank you!

14. sirm3d

thanks for the medal, @DarkendSinz30

15. Idealist

You're welcome.

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