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 uu 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 uu 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 uu 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

Options

A. `1/5`
B. `3/5`
C. `1/2`
D. `2/5`