Management Aptitude Test 2015 Paper

(b) Given, a bag contains 4 red and 3 black balls and second bag contains 2 red and 4 black balls.
From the two bag probability of selection of a bag = $\frac{1}{2}$
∴ Choose a red from the bag, P(getting a red ball)
= $\frac{1}{2}\times \frac{{}_{}^4{\mathit{C}}_1^{}}{{}_{}^7{\mathit{C}}_1^{}}+\frac{1}{2}\times \frac{{}_{}^2{\mathit{C}}_1^{}}{{}_{}^6{\mathit{C}}_1^{}}$
= $\frac{1}{2}\times \frac{4}{7}+\frac{1}{2}\times \frac{2}{6}$
= $\frac{4}{14}+\frac{1}{6}$
= $\frac{4\times 3+7\times 1}{42}$
= $\frac{12+7}{42}=\frac{19}{42}$