There is a spinner with the numbers 0 to 8 on it. There is another spinner with the numbers 0 to 6 on it. Both spinners are spun. What is the probability that the sum of the spins will be greater than 10?
The situation is continuous, not discrete. Please explain how you did it. Thanks.
2007-07-29 09:46:36 · 2 answers · asked by thyplo101 2 in Science & Mathematics ➔ Mathematics
It's easier to do this geometrically. Imagine a box of sides 8 and 6. Then imagine a line from (4,6) to (8,2). If a point is chosen at random and falls above this line, the sum is greater than 10. The area of the box is 6*8 = 48 while the area of the right triangle above this line is (1/2)4*4 = 8, so that the odds that the sum is greater (or equal to) 10 is 8/48, or 1/6.
For comparsion, let's say that the spinners have discrete integers from 0 to 6, and 0 to 8. Then there are 7^9 = 63 possible outcomes. But only 15 outcomes total up to 10 or greater, and only 10 total up to greater than 10. Hence, the respective odds would be 15/63 and 10/63.
2007-07-29 09:55:51 · answer #1 · answered by Scythian1950 7 · 1⤊ 0⤋
In order for the sum to be greater than 10, the number on the 0-8 spinner has to be 5 or more and the number on the 0-6 spinner has to be 3 or more. So we can write out the combinations
0-8 spinner........0-6 spinner
5..................... ..........6
6...................... ........5,6
7..................... .........4,5,6
8.................... ..........3,4,5,6
There are a total of 10 combinations each with a probability of (1/9)*(1/7) = 1/63. Therefore the probability is 10/63.
Math (and Stats) Rule!
2007-07-29 18:00:03 · answer #2 · answered by Math Chick 4 · 0⤊ 0⤋