+885 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.
+2489 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
