Probability

Consider three sets E1={1,2,3},F1={1,3,4} and G1={2,3,4,5}. Two elements are chosen at random, without replacement, from the set E1, and let S1 denote the set of these chosen elements.
Let E2=E1−S1 and F2=F1∪S1. Now two elements are chosen at random, without replacement, from the set F2 and let S2 denote the set of these chosen elements.
Let G2=G1∪S2. Finally, two elements are chosen at random, without replacement, from the set G2 and let S3 denote the set of these chosen elements.
Let E3=E2∪S3. Given that E1=E3, let p be the conditional probability of the event S1={1,2}. Then the value of p is