Problem:
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?
Answer Choices:
A. 12819​
B. 12823​
C. 41​
D. 12835​
E. 21​
Solution:
The result will occur when both A and B have either 0,1,2, or 3 heads, and these probabilities are shown in the table.
HeadsAB​081​161​​183​164​​283​166​​381​164​​​
The probability of both coins having the same number of heads is
81​⋅161​+83​⋅164​+83​⋅166​+81​⋅164​=12835​
Answer: D​.
The problems on this page are the property of the MAA's American Mathematics Competitions