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?

Show solution

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.