Question 1118549
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Formally, the definition of conditional probability is<br>
P(A|B) = (P(A and B))/(P(B))<br>
The way I think of conditional probability is that the sample space is only the outcomes in which B happens, so P(B) is the denominator of the probability fraction.  The numerator is then the probability that BOTH A and B happen.<br>
In your problem, the probability of getting white and then white is<br>
{{{P(WW) = (7/12)*(4/10) = 28/120}}}<br>
and the probability of getting black and then white is<br>
{{{P(BW) = (5/12)*(3/10) = 15/120}}}<br>
Then the probability that the first ball was white, given that the second ball was white, is<br>
{{{(28/120)/((28/120)+(15/120)) = 28/(28+15) = 28/43}}}