Question

An urn contains five balls alike in every respect save colour. If three of these balls are white and two are black and we draw two balls at random from this urn without replacing them. If A is the event that the first ball drawn is white and B the event that the second ball drawn is black, are A and B independent? If A and B are independent then enter 1, else enter 0.

Answer 1

Here $P\left(A\right)=\frac{3}{5},$

$P\left(B\right)=P\left(B/A\right)+P\left(B/B\right)=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}.$

Also $P(A\cap B)=\frac{3}{5}.\frac{2}{4}=\frac{3}{10}$

and $P\left(A\right)P\left(B\right)=\frac{3}{5}.\frac{3}{4}=\frac{9}{20}.$

Hence $P(A\cap B)\ne P\left(A\right)P\left(B\right).$Therefore A and B are not independent events.