Allison, Brian and Noah each have a 6-sided cube. All of the faces on Allison's cube have a 5. The faces on Brian's cube are numbered 1, 2, 3, 4, 5 and 6. Three of the faces on Noah's cube have a 2 and three of the faces have a 6. All three cubes are rolled. What is the probability that Allison's roll is greater than each of Brian's and Noah's? Express your answer as a common fraction.
+118613 Probability that Brian is less than 5 = 4/6 = 2/3
Probability that Brian is less than 5 = 3/6 = 1/2
Prob that both are less than 5 = $$\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right) = {\frac{{\mathtt{1}}}{{\mathtt{3}}}} = {\mathtt{0.333\: \!333\: \!333\: \!333\: \!333\: \!3}}$$
+709 I wish I knew... This sounds like something I learned in 5th grade. Sadly, I have already forgot many of the things I learned in elementary school.
+118613 Probability that Brian is less than 5 = 4/6 = 2/3
Probability that Brian is less than 5 = 3/6 = 1/2
Prob that both are less than 5 = $$\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right) = {\frac{{\mathtt{1}}}{{\mathtt{3}}}} = {\mathtt{0.333\: \!333\: \!333\: \!333\: \!333\: \!3}}$$
