Difference between revisions of "2004 AMC 10A Problems/Problem 10"
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Coin <math>A</math> is flipped three times and coin <math>B</math> is flipped four times. What is the probability that the number of heads obtained from flipping the two fair foins is the same? | Coin <math>A</math> is flipped three times and coin <math>B</math> is flipped four times. What is the probability that the number of heads obtained from flipping the two fair foins is the same? | ||
− | <math> \mathrm{(A) \ } \frac{29}{128} \qquad \mathrm{(B) \ } \frac{23}{128} \qquad \mathrm{(C) \ } \frac14 \qquad \mathrm{(D) \ } \frac{35}{128 | + | <math> \mathrm{(A) \ } \frac{29}{128} \qquad \mathrm{(B) \ } \frac{23}{128} \qquad \mathrm{(C) \ } \frac14 \qquad \mathrm{(D) \ } \frac{35}{128} \qquad \mathrm{(E) \ } \frac12 </math> |
==Solution== | ==Solution== | ||
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*[[2004 AMC 10A Problems/Problem 11|Next Problem]] | *[[2004 AMC 10A Problems/Problem 11|Next Problem]] | ||
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+ | [[Category:Introductory Combinatorics Problems]] |
Revision as of 11:07, 5 November 2006
Problem
Coin is flipped three times and coin is flipped four times. What is the probability that the number of heads obtained from flipping the two fair foins is the same?
Solution
There are 4 ways that the same number of heads will be obtained; 0, 1, 2, or 3 heads.
The probability of both getting 0 heads is .
The probability of both getting 1 head is
The probability of both getting 2 heads is
The probability of both getting 3 heads is
Therefore, the probabiliy of flipping the same number of heads is: