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I have some trouble to determine the probability of the following example There are 3 blue balls, 5 red balls, and 4 white balls in a bag of balls. If a person selects two of the balls, what is the probability that the second one is blue given that the first one was white?

A=White B= blue

p[B/A]=p[A and B]/p[A]= p[A]*p[B/A]/p[A]= 3/11

or P[B/A]= 4/12 * 3/11 = 1/11

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You don't actually have to use any of the more complex equations for this one (you might if you wanted A|B).

Given that the first ball was white, there are now 3 blue, 5 red and 3 white. So the chances of the second being blue is just $\frac{3}{3+5+3}=\frac{3}{11}$ i.e. the first answer.

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