There are two urns A and B. Urn A contains 5 red, 3 blue, and 2 white balls, urn B contains 4 red,3 blue, and 3 white balls. An urn is choosen at random and a ball is drawn. Probability that the ball drawn is red is

Let A and B, respectively, be the events that urn A and urn B are selected. Let R be the event that the selected ball is red. Since the urn is chosen at random, Therefore

$\mathrm{P}\left(\mathrm{A}\right)=\mathrm{P}\left(\mathrm{B}\right)=\frac{1}{2}$

and $\mathrm{P}\left(\mathrm{R}\right)=\mathrm{P}\left(\mathrm{A}\right)\mathrm{P}(\mathrm{R}/\mathrm{A})+\mathrm{P}\left(\mathrm{B}\right)\mathrm{P}(\mathrm{R}/\mathrm{B})$

 $=\frac{1}{2}\times \frac{5}{10}+\frac{1}{2}\times \frac{4}{10}=\frac{9}{20}$