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# Ant needs help!

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What is the probability that at least two of the faces match when you roll three fair six-sided dice? Express your answer as a common fraction.

ant101  Feb 20, 2018
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#1
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[6C2 * 6] / 6^3 = 90/216 =5 / 12

Guest Feb 20, 2018
#2
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noppppppppppppppppppppppppppppppppppeeeeeeeeeeeeeee

ant101  Feb 20, 2018
#3
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3C2 . 1/6 . 5/6 = 5/12

Guest Feb 20, 2018
#4
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It looks like the above answer is from Mr. BB or one of his students.

For this question, it’s easier to count the negations, i.e when there are no matches.

$$\small \text {There are six ways to roll the first die. (6)}\\ \small \text {There are five ways to roll the second die for it NOT to match the first. (5)}\\ \small \text {There are four ways to roll the third die for it NOT to match the first or second. (4) }\\ \small \text {So, there are } 6*5*4 = 120 \text { ways to roll three dice with NO matches. }\\ \small\text {And there are }6^3 \text {ways to roll all combinations. (216) }\\ \large 1- \dfrac {6*5*4}{216} = \dfrac{5}{9} \approx 44.44 \%$$

GA

GingerAle  Feb 21, 2018

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