In: Statistics and Probability
A specially made pair of dice has only one- and two-spots on the faces. One of the dice has three faces with a one-spot and three faces with a two-spot. The other die has two faces with a one-spot and four faces with a two-spot. One of the dice is selected at random and then rolled six times. If a two-spot shows up five times, what is the probability that it is the die with the three two-spots?
(Simplify your answer. Do not round until the final answer. Then round to four decimal places as needed.)