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?

0.407

Step-by-step explanation:

Let A be the event that you pull out the 6-sided dice, and B be the event that the out come of the roll is 4.

There are 3 dices with equal chance of getting pull out so P(A) = 1/3.

There are 3 ways to roll a 4 out of 4 + 6 + 12 = 22 options of 3 die. So P(B) = 3/22.

A|B is the event that you pull out the 6-sided dice, knowing that the out come of the roll is 4.

B|A is the event that the outcome of the roll is 4, knowing that you pull out the 6-sides dice, so P(B|A) = 1/6

Using bayes conditional theorem, we have

45

step-by-step explanation:

30+15

rounding to the nearest thousandth would be 452,000