Browse · harp
Printimc
counting and probability intermediate
Problem
Two eight-sided dice each have faces numbered through . When the dice are rolled, each face has an equal probability of appearing on the top. What is the probability that the product of the two top numbers is greater than their sum?
(A)
(B)
(C)
(D)
Solution
We have , hence if at least one of the numbers is , the sum is larger. There such possibilities. We have . For we already have , hence all other cases are good. Out of the possible cases, we find that in the sum is greater than or equal to the product, hence in cases the sum is smaller, satisfying the condition. Therefore the answer is .
Final answer
C