Question 1020953: An experiment consists of recording the number of pins knocked down on each roll during a frame of a bowling game. A bowler may take maximum of two rolls per frame. How many outcomes are in the sample space for this experiment (hint: if the first roll is a 10 (strike), the experiment is over.
Answer by FrankM(1040)   (Show Source):
You can put this solution on YOUR website! 
The first roll is the top line of numbers 0-10, then the second roll is down the left side. The totals appear in the grid. This is the same as finding the outcomes for the roll of 2 dice, except, of course, there are 10 pins, so it's 0-10.
Now, as you know, the maximum can be just 10, so I made red the numbers that are not valid.
We are left adding the results that remain. add 1+2+3+.....11 = 66 possible results. But, the 10 at the end of the top results has to be discarded, if you roll 10 you can't have a second roll. So 65 results.
I hope this is clear, once we get the valid results we are not adding the numbers themselves, just the number of valid boxes, i.e. 11 on the top line reduced to 10, then next line 10, then 9, etc.
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