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Solved Example #4

Saturday, February 9th, 2013

Question : There are 4 red & 5 green balls in bag A and 5 red & 6 green balls in bag B. If a bag is selected at random and a ball is selected from that, what is the probability that it is red?

Answer : 

Probability of Red Ball = Bag A is selected & Red Ball is selected + Bag B is selected & Red Ball is selected

ie.

(1/2)*(4/9) + (1/2)*(5/11) =  (1/2)[ (44+45) / 99 ] = 89/198