Box A contains 2 black and 3 red balls, while Box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random; and the probability of choosing Box A is double that of Box B . If a red ball is drawn from the selected box, then the probability that it has come from Box B , is

Step-by-step solution

Let P(B)=p according to given condition aligned P(A) & =2 P(B)=2 p P ( R A ) & = ^3 C₁ ^5 C₁ = 3 5 aligned and P ( R B )= ^4 C₁ ^7 C₁ = 4 7 Using Baye's theorem aligned P ( B R ) & = P(B) P ( R B ) P(A) P ( R A )+P(B) P ( R B ) & = p 4 7 2 p 3 5 +p 4 7 & = 4 7 6 5 + 4 7 = 4 7 42+20 35 & = 20 62 = 10 31 aligned