Bunuel wrote:
Two six-sided dice with sides numbered 1 through 6 are rolled. If the two resulting numbers are multiplied, what is the probability that their product will be even?
A. 1/12
B. 1/4
C. 1/2
D. 3/4
E. 11/12
There are two tricks to this one.
The first is to realize what 'product is even' really means. It's really asking you for the probability that one or both numbers are even. If you're calculating products, you're solving this one incorrectly.
The second has to do with strategies for solving probability problems. To find a complicated probability ('one or both'), there are two basic approaches. One possibility is to divide up the probability into multiple smaller probabilities, then add or multiply those together as appropriate. In this case, you'd find three probabilities that don't overlap with each other:
- The probability that the first die is even and the second is odd;
- The probability that the first die is odd and the second is even;
- The probability that they're both even.
Then add those three up and you have your answer.
However, there's a quicker approach. If you can find the 'opposite' of your probability - the probability that it
won't happen - you can just subtract that number from 1 to get your answer. In this problem, the only situation where the product
won't be even is if both dice are odd. The probability of the first die being odd is 1/2, the probability of the second die being odd is 1/2, and so the probability that both are odd is 1/2 * 1/2 = 1/4. Then the answer to the question is 1-1/4 = 3/4.
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