Correct option is (c) 16/31
The explanation is: Let E1 = event of choosing the bag 1, E2 = event of choosing the bag 2.
Let A be event of drawing a red ball.
P(E1) = P(E2) = 1/2.
Also, P(A|E1) = P(drawing a red ball from Bag 1) = 3/8.
And P(A|E2) = P(drawing a red ball from Bag 2) = 4/10.
The probability of drawing a ball from bag 2, being given that it is red is P(E2|A).
By using Bayes’ theorem,
P(E2|A) = P(E2)P(A|E2)/( P(E1)P(A│E1)+P(E2)P(A|E2))
= (1/2 × 4/10) / ((1/2 × 3/8)) + (1/2 × 4/10)) = 16/31.