Consider three sets E 1 = 1 , 2 , 3 , F 1 = 1 , 3 , 4 and G 1 = 2 , 3 , 4 , 5 . Two elements are chosen at random, without replacement, from the set E 1 , and let S 1 denote the set of these chosen elements. Let E 2 = E 1 - S 1 and F 2 = F 1 ∪ S 1 . Now two elements are chosen at random, without replacement, from the set F 2 and let S 2 denote the set of these chosen elements. Let G 2 = G 1 ∪ S 2 . Finall

Step-by-step solution

We need to find p , the conditional probability of the event S 1 = 1 , 2 , given E 1 = E 3 . So, p = P S 1 ∩ E 1 = E 3 P E 1 = E 3 = P B 1 , 2 P ( B ) P ( B ) = P B 1 , 2 + P B 1 , 3 + P B 2 , 3 P B 1 , 2 → If 1 , 2 chosen in the beginning P B 1 , 3 → If 1 , 3 chosen in the beginning P B 2 , 3 → If 2 , 3 chosen in the beginning (i) If 1 , 2 is chosen in the begining, then F 2 = 1 , 2 , 3 , 4 and S 2 must contain 1 and S 3 = 1 , 2 from G 2 = 1 , 2 , 3 , 4 , 5 So, P B 1 , 2 = 1 3 × 1 &#21