SOLUTION: Box A contains nine cards numbered 1 through 9,and box B contains five cards numbered 1 through 5. A box is chosen at random and a card is drawn. If the number is even find the pro

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Question 1143226: Box A contains nine cards numbered 1 through 9,and box B contains five cards numbered 1 through 5. A box is chosen at random and a card is drawn. If the number is even find the probability that the card came from Box A.
Found 2 solutions by 4419875, ikleyn:
Answer by 4419875(21)   (Show Source): You can put this solution on YOUR website!
There is 1/2 chance of choosing box a and 4/9 of balls from it. Even={2,4,6,8}
Hence,
Answer by ikleyn(52799)   (Show Source): You can put this solution on YOUR website!
.
Box A contains nine cards numbered 1 through 9,and box B contains five cards numbered 1 through 5.
A box is chosen at random and a card is drawn. If the number is even find the probability that the card came from Box A.
~~~~~~~~~~~~~~~~~~~~


            The solution by the other post answers the question: 
                What is the probability to get an even number from box A ?

            But the question in the problem is  TOTALLY  DIFFERENT,  so that solution is  IRRELEVANT.

            Below find the correct solution. 


By the definition, the conditional probability is

    P(A) = P(even,A)/P(even,A+B),

where  P(A)        is the probability under the question that the number came from box A provided that it is even;

       P(even,A)   is the probability to get even number from box A;

       P(even,A+B) is the probability to get even number from either box A or box B.


Box A contains 9 numbers; of them, 4 numbers are even.
Box B contains 5 numbers; of them, 2 numbers are even.


Therefore, we have

    P(even,A+B) =  =  = ;

    P(even,A)   = .


Therefore,

    P(A) =  =  =  = 0.5263 = 52.63%  (approximately).     ANSWER



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