2002 AMC 12P Problems/Problem 15
- The following problem is from both the 2002 AMC 12P #15 and 2002 AMC 10P #17, so both problems redirect to this page.
Problem
There are red marbles and black marbles in a box. Let be the probability that two marbles drawn at random from the box are the same color, and let be the probability that they are different colors. Find
Solution
First we find the value of . Note that whatever color we choose on our first marble, there are exactly of marbles remaining that match that color. Therefore, .
Now we find the value of . Again, the actual color of the first marble does not matter, since there are always exactly of marbles remaining that don't match that color. Therefore, .
The value of is therefore .
~Minor edits from Astro2010~
See also
2002 AMC 10P (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
2002 AMC 12P (Problems • Answer Key • Resources) | |
Preceded by Problem 14 |
Followed by Problem 16 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.