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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, form 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 . Finally, two elements are chosen at random, without replacement, from the set G 2 and let S 3 denote the set of these chosen elements. Let E 3 = E 2 ∪ S 3 . Given that E 1 = E 3 , let p be the conditional probability of the event S 1 = {1, 2}. Then the value of p is

1. 5 1
2. 5 3
3. 2 1
4. 5 2

Correct answer: 5 1

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