Problem:
A box contains chips, numbered , and . Chips are drawn randomly one at a time without replacement until the sum of the values drawn exceeds . What is the probability that draws are required?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Three draws will be required if and only if the first two chips drawn have a sum of 4 or less. The draws , , and are the only draws meeting this condition. There are possible two-chip draws, so the requested probability is . (Note that all possible two-chip draws are considered in determining the denominator, even though some draws will end after the first chip is drawn.)
The problems on this page are the property of the MAA's American Mathematics Competitions