A box contains ten balls, numbered 1-10. Marisha reaches in without looking and draws a ball. The Penny draws a ball without looking. What is the probability that the sum of the numbers is greater than 8.
Okay. First, there are 24 possible ways of drawing balls that have a sum of less than 8. These are listed below:
1,2 1,3 1,4 1,5 1,6 1,7
2,1 2,3 2,4 2,5 2,6
3,1 3,2 3,4 3,5
4,1 4,2 4,3
5,1 5,2 5,3
6,1 6,2
7,1
Note that because Penny is choosing one and Marisha is choosing the other and it matters which one each of them choose that (for instance) 1,7 and 7,1 are separate possibilities.
Now, there are 10 balls to choose from for Marisha. After Marisha chooses, there will be 9 balls remaining for Penny to choose from. There are not 10 remaining because Marisha does not return the ball she has chosen back into the box before Penny chooses hers. The total number of ball-choosing combinations can be found by multiplying the number of options Marisha has by the number of options that Penny has:
10 x 9 = 90
So there are 90 possible combinations, and as we found earlier, 24 of them have sums of less than or equal to 8. Therefore, 66 combinations out of 90 combinations have a sum of more than 8.
Your probability will be found by dividing 66 applicable combinations into 90 total combinations:
66/90 which can be simplified to 11/15.
Answer: The probablity of the sum being greater than 8 is 11/15.