Problem:
For a particular peculiar pair of dice, the probabilities of rolling 1,2,3,4,5, and 6 on each die are in the ratio 1:2:3:4:5:6. What is the probability of rolling a total of 7 on the two dice?
Answer Choices:
A. 634
B. 81
C. 638
D. 61
E. 72
Solution:
On each die the probability of rolling k, for 1≤k≤6, is
1+2+3+4+5+6k=21k
There are six ways of rolling a total of 7 on the two dice, represented by the ordered pairs (1,6),(2,5),(3,4),(4,3),(5,2), and (6,1). Thus the probability of rolling a total of 7 is
2121⋅6+2⋅5+3⋅4+4⋅3+5⋅2+6⋅1=21256=638
The problems on this page are the property of the MAA's American Mathematics Competitions