A box contains 3 blue and 2 red marbles while another box contains 2 blue and 5 red marbles.
A marble drawn at random from one of the boxes turns out to be blue. What is the probability that it came from the first box?
You are told to use Bayes Theorem. I have tried to but never get the right answer.
Please explain fully.
A marble drawn at random from one of the boxes turns out to be blue. What is the probability that it came from the first box?
You are told to use Bayes Theorem. I have tried to but never get the right answer.
Please explain fully.
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P[box 1 & blue] = 1/2 * 3/5 = 3/10 = 21/70
P[box 2 & blue] = 1/2 * 2/7 = 1/7 = 10/70
P[blue] = sum of the above = 31/70
P[box 1 | blue] = P[box 1 & blue] /P[blue]
= [21/70] / [ 31/70]
= 21/31
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P[box 2 & blue] = 1/2 * 2/7 = 1/7 = 10/70
P[blue] = sum of the above = 31/70
P[box 1 | blue] = P[box 1 & blue] /P[blue]
= [21/70] / [ 31/70]
= 21/31
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it is simpler version of bayes' th.
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