HW Help...Suppose you roll two 6-sided die, one red and one blue....

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mariposies

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Please help with this HW problem Part A says:

Suppose you roll two 6-sided die, one red and one blue.
(a) How many individual outcomes are there (treat the red and blue dice as being different)?
I know that the answer to this is 36


(b) If you only care about the total of the two dice, how many individual outcomes are there? (This part of the problem is confusing, how is total of two dice different from individual outcomes listed in Part A?

Thank you for your assistance !
 
mariposies said:
Suppose you roll two 6-sided die, one red and one blue.
(a) How many individual outcomes are there (treat the red and blue dice as being different)?
I know that the answer to this is 36

(b) If you only care about the total of the two dice, how many individual outcomes are there? (This part of the problem is confusing, how is total of two dice different from individual outcomes listed in Part A?
Click to expand...
Look at the ordered pair \(\displaystyle (R,B) \) where \(\displaystyle R \) is the number showing on the red die and \(\displaystyle B \) is the number showing on the blue die. There are six outcomes for both dice. So where does the 36 come in?

If for each pair we add the numbers, \(\displaystyle R+B \), how many different sums do we have?
That answers the part b).
 
mariposies said:
Suppose you roll two 6-sided die, one red and one blue.
(a) How many individual outcomes are there (treat the red and blue dice as being different)?
I know that the answer to this is 36
Click to expand...
Good. Now draw the six-by-six table which generates these thirty-six outcomes, like they did in class or in the book, listing the outcomes for each die along the sides (like you used to do, back in grammar school, for multiplication tables):

Code: 
# | 1 | 2 | 3 | 4 | 5 | 6 |
--*---*---*---*---*---*---*
1 |   |   |   |   |   |   |
--*---*---*---*---*---*---*
2 |   |   |   |   |   |   |
--*---*---*---*---*---*---*
3 |   |   |   |   |   |   |
--*---*---*---*---*---*---*
4 |   |   |   |   |   |   |
--*---*---*---*---*---*---*
5 |   |   |   |   |   |   |
--*---*---*---*---*---*---*
6 |   |   |   |   |   |   |
--*---*---*---*---*---*---*

mariposies said:
(b) If you only care about the total of the two dice, how many individual outcomes are there?
Click to expand...
Fill in your table with the sums. Note the entries; some are duplicates. For instance, Red1 + Blue3 = 4, as does Red2 + Blue2. Cross off all but one of each value for which there are duplicates. (Remember: You only care about the sum, not the inputs nor the colors.) Then count up the number of individual outcomes remaining. ;)
 
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