If you roll three fair six-sided dice, what is the probability that the product of the three numbers rolled is even?
A) 1/8 B) 1/6 C) 1/2 D) 5/6 E) 7/8 ANSWER: Choice E (7/8) 1) The total number of possible outcomes of rolling three fair six-sided dice would be 216. This is because there are 6 outcomes for each dice (6*6*6 = 216) 2) First off...the word "Product" indicates the result from multiplication. So, we are going to look at possible Multiplication Outcomes: (EVEN #)*(EVEN #)*(EVEN #) = EVEN# (ODD #)*(EVEN #)*(EVEN #) = EVEN# (ODD #)*(ODD #)*(EVEN #) = EVEN# (ODD #)*(ODD #)*(ODD#) = ODD# ---> The only way in multiply three numbers to get an odd number 3)It actually would be easier to find the probability of rolling three numbers with an "odd" product because there is only one way to multiply three numbers to get an odd number 4) On each of the three dice the only odd numbers are 1, 3, and 5. The total possible combinations with getting these three odd numbers is 3*3*3 = 27 possible combinations. Therefore, the probability of getting an odd product is 27/216, which reduces to 1/8. 5) Ergo, because the only other option is getting an even product, the probability of rolling three numbers with an even product is 1-1/8 = 8/8-1/8 = 7/8-->Choice E
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Math Problem of the Day ANSWERS PART II
Here are the solutions to The Math Problems of The Day. The problems and solutions shown here come
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