Math Is Fun Forum

Q. there are two bags A and B; bag A contains 2 white and 3 black balls; bag B contains 3 white and 4 black balls. A bag is chosen at random find the probability that the ball drawn is white.

My answer : I am OK with P(W) = P(A,W)+ P(B,W)= 1/2 * 2/5 + 1/2 * 3/7 = 29/70 OK !!

but if I want to solve the same problem using the classical approach,

           n(E)    number of ways of selecting white ball   
P(W) = ---- = ---------------------------------------------- then what ????
           n(s)    total number of ways of drawing a ball

I think! the no. of selecting white balls should be = (number of ways of selecting a bag = 2) * [(either take white ball from A = 2
                                                                                                                                    |
                                                                                                                                   and

ways) + (either take white ball from B = 3 ways)]= 10 ways ----------------------- but I know it is wrong.
          |
         or

I am confused and unable about Finding the number of ways of selecting white balls and total number of ways of drawing a balls.

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the conditional probability problems can not be solved using n(E)/n(S) approach ??????? ------- but why ??

Please help me soon I am in a great need of it Thanks in advance.