help

1 5

5 1

4 2

2 4

3 3        5 possibles out of 36 possible rolls        5/36     5/36 = .1389

You roll two dice. What is the probability that the average of the high and low roll is exactly 3, to four decimal places?   

The first die can be one of six numbers. 

For each of those six numbers, the second die can be one of six numbers.

Thus, there are a total 36 possibilities that the two dice can land.

To average the total of the numbers that the two dice land on, you have to divide by two. 

Thus, to average three, the total has to be six.

How many ways are there to roll a six?  There are five ways:  1-5, 2-4, 3-3, 4-2, and 5-1 

So the likelihood of rolling a total of six is 5 opportunities out of 36 possibilities.

That's written as 5/36 which, to four decimal places, quotients out to 0.1389 or 13.8889% if that's the form the problem wants.   

I see a possible flaw.  One of the possibilities is to roll a 3-3.  Since they're the same value, there is no "high" and "low".

If this is to be taken into account, then the probability would be 4/36.  You can do the arithmetic to get it in decimal form.

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