I roll two standard six-sided fair dice. At least one of the scores obtained on the dice is 3. What is the probability that both of the scores on the dice are 3?
A. 1/12
B. 1/11
C. 1/6
D. 1/3
E. 1/4
B. 1/11
There are 36 different equally likely possible outcomes (a, b) for the two dice. The number of these which involve only 1, 2, 4, 5 or 6 is 5 × 5 = 25.
So there are just eleven involving a 3, one of which is (3, 3).
So the probability that both are 3, given that at least one is 3, is 1/11.
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