Question

Three urns A, B and C contain 6 red and 4 white ; 2 red and 6 white ; 1 red and 5 white balls respectively. An urn is chosen at random and a ball is drawn. If the ball drawn is found to be red, find the probability that the ball was drawn from urn A.

Answer 1

$P(W_1,W_2)+P(R_1,R_2)+P(B_1,B_2)$

mans,

$P(W_1$ intersection $W_2)+P(R_1\cap R_2)+P(B_1\cap B_2)$

$P\left(W_1\right)=\frac{5}{12},P\left(W_2\right)=\frac{5}{18}$

$P\left(R_1\right)=\frac{4}{12},P\left(R_2\right)=\frac{6}{18}$

$P\left(B_1\right)=\frac{3}{12},P\left(B_2\right)=\frac{7}{18}$

Since it is a case of in dependents as one think of and in such case we can reach to the answer of the question.

Requited prob. = $\frac{5}{12}\times \frac{5}{18}+\frac{4}{12}\times \frac{6}{18}+\frac{3}{12}\times \frac{7}{18}$

$=\frac{70}{216}=\frac{35}{108}$