Bag A contains 3 white, 7 red balls and bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A , if the ball drawn in white, is :

Step-by-step solution

Given: Given balls in bags are A → 3 W , 7 R , B → 3 W , 2 R Let, E 1 : A is selected , E 2 : B is selected and E : white ball is drawn Using Baye's theorem, ⇒ P E 1 E = P ( E 1 ) · P E E 1 P E 1 · P E E 1 + P E 2 · P E E 2 ⇒ P E 1 E = 1 2 × 3 10 1 2 × 3 10 + 1 2 × 3 5 ⇒ P E 1 E = 3 20 3 20 + 6 20 ⇒ P E 1 E = 3 3 + 6 ⇒ P E 1 E = 1 3