Suppose a game show called Bayesian Boxes has the contestant sample one marble from a box and guess what type of box it is. When the contest

Question

Suppose a game show called Bayesian Boxes has the contestant sample one marble from a box and guess what type of box it is. When the contestant picks a box, the chance of each box type for this round is as follows:
Type A: 75%, Type B: 20%, and Type C: 5%
The chance of drawing a red marble from Type A is 2%, from Type B is 25%, and from Type C is 98%.
The contestant selects a box and draws a marble. What is the chance of drawing a red marble? (Give the exact decimal answer.)
If the contestant does draw a red marble, what is the chance it came from box Type C? (Give the decimal answer rounded to at least four places.)

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Tryphena 1 year 2021-08-27T15:29:31+00:00 1 Answers 0 views 0

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    2021-08-27T15:31:04+00:00

    Answer:

    0.114

    0.049

    Step-by-step explanation:

    For the boxes:

    Type A – 75% = 0.75

    Type B – 20% = 0.2

    Type C – 5% = 0.05

    For the marbles in each box:

    Type A – 2% = 0.02

    Type B – 20% = 0.25

    Type C – 98% = 0.98

    Then you can multiply the chance of drawing each box by the chance of drawing a red marble from that box and add all of those together:

    0.75 * 0.02 + 0.2 * 0.25 + 0.05 * 0.98

    = 0.015 + 0.05 + 0.049

    = 0.114

    The specific chance for box Type C is 0.05 * 0.98 = 0.049

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