Problem:
The students at King Middle School are divided into three groups of equal size for lunch. Each group has lunch at a different time. A computer randomly assigns each student to one of the three lunch groups. The probability that three friends, Al, Bob, and Carol, will be assigned to the same lunch group is approximately
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Al must be assigned to one of the lunch groups. The probability that Bob is assigned to the same Iunch group is approximately ( exactly) and the probability that Carol is assigned to that same group is also approximately . Thus the probability that all three are assigned to the same group is approximately .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions