Three urns contain 6 red, 4 black; 4 red, 6 black and 5 red, 5 black marbles respectively. One of the urns is selected at random and a marble is drawn from it. If the marble drawn is red, then the probability that it is drawn from the first urn is

$\frac{2}{5}$

no. of urns = 3

$P(U_1) = \frac{1}{3} = P(U_2) = P(U_3)$

U_i → selecting i^th urn

$P(\frac{U_1}{R}) = \frac{P(U_1) P(\frac{R}{U_1})}{\sum\limits_{i=1}^{3} P(U_i) P(\frac{R}{U_i})} = \frac{\frac{1}{3} \times \frac{6}{10}}{\frac{1}{3} \times \frac{6}{10}+\frac{1}{3} \times \frac{4}{10}+1 \times \frac{5}{10}}$

$= \frac{6}{15} = \frac{2}{5}$

Option: 4