I have a bag with 3 fair dice. One is 4-sided, one is 6-sided, and one is 12-sided. I reach into the bag, pick one at random and roll it. The outcome of the roll is 4. What is the probability that I pulled out the 6-sided die?
The probability of pulling one of the dice at random = 1 / 3
If its the 6-sided die, then the probability of of rolling a 4 = 1/6
Therefore, the probability that rolling a 4 comes from a 6-sided die = 1 / 3 x 1 / 6 = 1 / 18 =~5.55 %
