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 \(\cup\) 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 \(\cup\) 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 \(\cup\) S₃. Given that E₁ = E₃, let p be the conditional probability of the event S₁ = {1, 2}. Then the value of p is