In a dice game, a player rolls two dice. His score is the larger of the two numbers on the dice. For example, if he rolls 3 and 5 , his score is 5 , and if he rolls 4 and 4 , his score is 4 . What is the probability that his score is 3 or less?
(A) $\frac{1}{4}$
(B) $\frac{7}{36}$
(C) $\frac{5}{36}$
(D) $\frac{1}{3}$
(E) $\frac{2}{9}$
When a player rolls two dice, there are 6 possibilities for the outcome on each die, so there are 36 possibilities for the outcomes when two dice are rolled.

Which possibilities give a score of 3 or less? These are: 1 and 1,1 and 2,1 and 3, 2 and 1,2 and 2,2 and 3, 3 and 1,3 and 2,3 and 3. So 9 of the 36 possibilities give a score of 3 or less. Thus, the probability is $\frac{9}{36}=\frac{1}{4}$.