Consider three sets E 1 = 1, 2, 3 , F 1 = 1, 3, 4 and G 1 = 2, 3, 4, 5 . Two elements are…

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