Probability
posted by Bart on .
Sharon was palying darts. She threw six darts and all of them hit the target. Which of the following could be her score?
The target goes from 9 in the center, then 7, 5 , 3, and 1 on the outside ring.
Possible Scores: 4 17 56 28 29 31 50 8
Please give a quick explanation.

Without seeing where the darts hit, there is no way we can tell the score she got. You can, however, eliminate some of the "possible scores" because there is no way you can get certain totals in six throws, of yopu score on each throw.
4, 50 and 56 are not possible. The total has to be between 6 and 42, inclusive.
That leaves 8, 17, 28, 29, 31 as possibilities. Now you can also eliminate 17, 29 and 31 because the sum of four odd numbers must be even.
That leaves 8 and 28. See if you can think of a way to get either score.
1 + 1 + 1 + 1 + 1 + 3 = 8
7 + 7 + 7 + 5 + 1 + 1 = 28 
9+9+9+9+9+5 = 50 which is a possible score.