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jmc

counting and probability junior

Problem

Nathan will roll two six-sided dice. What is the probability that he will roll a number less than three on the first die and a number greater than three on the second die? Express your answer as a common fraction.
Solution
For the first die to be less than three, it must be a 1 or a 2, which occurs with probability . For the second die to be greater than 3, it must be a 4 or a 5 or a 6, which occurs with probability . The probability of both of these events occuring, as they are independent, is .
Final answer
\frac{1}{6}