2004 AMC 10A Problem 10

Coin

A

is flipped three times and coin

B

is flipped four times. What is the probability that the number of heads obtained from flipping the two fair coins is the same?

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Solution

The two coins match when both show

0,

1,

2,

3

heads. Coin

A

has weights

1, 3, 3, 1

out of

8

and coin

B

has weights

1, 4, 6, 4, 1

out of

16.

The probability is

\begin{aligned} &\dfrac{1\cdot 1 + 3\cdot 4 + 3\cdot 6 + 1\cdot 4}{8 \cdot 16} \\ &= \dfrac{35}{128}. \end{aligned}

Thus, the correct answer is D.

Tagged: binomial probability · casework