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. Th

Question

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?

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Arya 1 week 2022-01-12T06:49:24+00:00 1 Answer 0 views 0

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    2022-01-12T06:50:51+00:00

    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

    P(A|B) = \frac{P(B|A)P(A)}{P(B)} = \frac{\frac{1}{6}\frac{1}{3}}{\frac{3}{22}}

    P(A|B) = \frac{1}{18}\frac{22}{3} = 0.407

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