SOLUTION: Two fair dice are tossed. Find the odds against the sum being less than 4.

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Question 865097: Two fair dice are tossed. Find the odds against the sum being less than 4.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!



⚀⚀   ⚀⚁   ⚀⚂   ⚀⚃   ⚀⚄   ⚀⚅

⚁⚀   ⚁⚁   ⚁⚂   ⚁⚃   ⚁⚄   ⚁⚅

⚂⚀   ⚂⚁   ⚂⚂   ⚂⚃   ⚂⚄   ⚂⚅

⚃⚀   ⚃⚁   ⚃⚂   ⚃⚃   ⚃⚄   ⚃⚅

⚄⚀   ⚄⚁   ⚄⚂   ⚄⚃   ⚄⚄   ⚄⚅

⚅⚀   ⚅⚁   ⚅⚂   ⚅⚃   ⚅⚄   ⚅⚅

The red dice rolls ARE less than 4.
  
The blue ones are NOT less than 4.

Since it's odds AGAINST, count the blue ones first.

There are 33 of them. So we write that number first

33

Then after the 33 we put either a colon ":" or else the word "to".

33:   or  33 to

Next we count the red ones.

There are 3 of them.  So we write the number 3 after the colon or the
word "to":

33:3   or  33 to 3.

Now since you can divide both the 33 and the 3 by 3, you can write those
as

11:1   or  11 to 1.

Edwin