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.
HeadsAB081161183164283166381164
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