SOLUTION: 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 ar

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(52777) (Show Source): You can put this solution on YOUR website!
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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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