GATE | GATE-CS-2005 | Question 51

Box P has 2 red balls and 3 blue balls and box Q has 3 red balls and 1 blue ball. A ball is selected as follows:

(i)  Select a box
(ii) Choose a ball from the selected box such that each ball in
     the box is equally likely to be chosen. The probabilities of
     selecting boxes P and Q are (1/3) and (2/3), respectively.  

Given that a ball selected in the above process is a red ball, the probability that it came from the box P is
(A) 4/19
(B) 5/19
(C) 2/9
(D) 19/30


Answer: (A)

Explanation:

The probability of selecting a red ball  = 
              (1/3) * (2/5) + (2/3) * (3/4) = 2/15 + 1/2 
              = 19/30  [Let it be P1]

Probability of selecting a red ball from box P =
             (1/3) * (2/5) = 2/15 [Let it be P2]

Given that a ball selected in the above process is 
a red ball, the probability that it came from the 
box P is = P1/P2 = (2/15) / (19/30) = 4/19 


Quiz of this Question

My Personal Notes arrow_drop_up
Article Tags :

1


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.