Question 1200461: A store purchases baseball hats from three different manufacturers. In manufacturer A's box, there are 12 blue hats, 6 red hats, and 6 green hats. In manufacturer B's box, there are 10 blue hats, 10 red hats, and 4 green hats. In manufacturer C 's box, there are 8 blue hats, 8 red hats, and 8 green hats. A box is selected at random, and a hat is selected at random from that box. If the hat is red, find the probability that it came from manufacturer A's box.
Answer by ikleyn(52903)   (Show Source):
You can put this solution on YOUR website! .
A store purchases baseball hats from three different manufacturers.
In manufacturer A's box, there are 12 blue hats, 6 red hats, and 6 green hats.
In manufacturer B's box, there are 10 blue hats, 10 red hats, and 4 green hats.
In manufacturer C 's box, there are 8 blue hats, 8 red hats, and 8 green hats.
A box is selected at random, and a hat is selected at random from that box.
If the hat is red, find the probability that it came from manufacturer A's box.
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This problem is on conditional probability.
They want you find the probability that a red hat is from box A given that
it is red, P(red hat is from box A | the hat is red).
This probability is the ratio
P(red hat is from box A | the hat is red) =  . (*)
The numerator is
P(red hat is from box A) =  =  =  .
The denominator is
P(the_hat_is_red) =  =
=  =  =  .
Therefore, the final probability (*) is
P(red hat is from box A | the hat is red) =  =  =  . ANSWER
Solved.
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