Dice A has 4 red and 2 white faces whereas dice B has 3 red and 3 white faces. A coin is tossed once, if it falls head then the game continues by throwing the dice A and if it falls tail then the dice B is to be used. If red turns up at first 3 throws, then the probability that dice A is being used is

Step-by-step solution

R → Red turns up at first three throws A → Dice A is selected. P A = 1 2 B → Dice B is selected. P B = 1 2 Using Bayes theorem, we get, P A R = P A ∩ R P R = P A × P R A P A × P R A + P B P R B = 1 2 × 2 3 3 1 2 × 2 3 3 + 1 2 1 2 3 = 64 91