2007 AMC 8 Problems/Problem 21
Problem
Two cards are dealt from a deck of four red cards labeled , , , and four green cards labeled , , , . A winning pair is two of the same color or two of the same letter. What is the probability of drawing a winning pair?
Video Solution
https://youtu.be/OOdK-nOzaII?t=1698
Solution 1
There are 4 ways of choosing a winning pair of the same letter, and ways to choose a pair of the same color.
There's a total of ways to choose a pair, so the probability is .
Solution 2
Notice that, no matter which card you choose, there are exactly 4 cards that either have the same color or letter as it. Since there are 7 cards left to choose from, the probability is . theepiccarrot7
See Also
2007 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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 AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.