2021 AMC 12A Problems/Problem 6
Contents
Problem
A deck of cards has only red cards and black cards. The probability of a randomly chosen card being red is . When
black cards are added to the deck, the probability of choosing red becomes
. How many cards were in the deck originally?
Solution
If the probability of choosing a red card is , the red and black cards are in ratio
. This means at the beginning there are
red cards and
black cards.
After black cards are added, there are
black cards. This time, the probability of choosing a red card is
so the ratio of red to black cards is
. This means in the new deck the number of black cards is also
for the same
red cards.
So, and
meaning there are
red cards in the deck at the start and
black cards.
So the answer is .
Note
See problem 1.
See also
2021 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 5 |
Followed by Problem 7 |
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 |
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