Question

Quick Question. Will fan and medal!

Answer 1

Roll 2 dice Look at the sum of the 2 dice. What is the probability of exactly one die is a 6 and the sum = 8?

Answer 2

The answer is 1/18 but I need an explanation

Answer 3

How many ways can the sum be 8? List all possible combinations of die rolls that add to 8.

Also list all possible die rolls where exactly one of them is a 6.

Answer 4

Possible die rolls where one is 6 is 6,1 6,2 6,3 6,4 6,5 or 5c2

sum of 8 are 3c2 I believe

Answer 5

so 12 possibilities for having a 6 as a number and 6 possibilities for a sum of 8

Answer 6

btw this is usually the easiest way to deal with two die questions:
http://www.scimathmn.org/stemtc/sites/default/files/images/frameworks/math/6.4.1A/image008.jpg

just count how many satisfy your conditions, and how many total outcomes there are.

Answer 7

If the sum is 8 and one die is 6 there are exactly two ways this could happen:
Die 1 = 6 and Die 2 = 2 or
Die 1 = 2 and Die 2 = 6
2/36=1/18

Answer 8

Oh, merts is right, this is sum of 8 AND exactly one is a 6. Not OR.

Answer 9

That makes sense...

Answer 10

How would I show work?

Answer 11

Just show the possible outcomes:

6,2
2,6

And total outcomes is...

Answer 12

If you're doing it with combinations,
\[\frac{ 2C1 }{6C1}*\frac{ 1C1 }{6C1 }\]
Since from two die outcomes (a 6 or a 2), you're picking one, then there's only one left

Though using combinations sometimes can make things more difficult than need be. It doesn't save any effort here.

Answer 13

Thanks!

Answer 14

You're welcome. I'd just show the work by listing the two possible outcomes 6,2 and 2,6, and the total number of outcomes 36. It's much easier for someone grading your work to follow that.

Answer 15

Alrighty I'll do it that way