Answer:
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
[tex]P(A|B) = \frac{P(B|A)P(A)}{P(B)} = \frac{\frac{1}{6}\frac{1}{3}}{\frac{3}{22}}[/tex]
[tex]P(A|B) = \frac{1}{18}\frac{22}{3} = 0.407[/tex]
