in a certain game, a player throws a standard 6 sided number cube twice per turn. what is the probability that the results of the first throw will be a 5 or a 6, and the second throw will be an even number?
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Since both events are independent, we have that, the sum of the events over the total number of events gives the probability (for each individual one). Hence, the probability of this happening is: \[ \left(2\cdot \frac{1}{6}\right)\cdot\left(3\cdot \frac{1}{6}\right)=\frac{1}{6} \]Since 5 and 6 are two of six possibilities and an even number is three of six.
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