Consider three sets $$E_1 = \left\{1, 2, 3 \right\}, F_1 = \left\{1, 3, 4 \right\}$$ and $$G_1 = \left\{2, 3, 4, 5 \right\}$$. 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 $$F_2 = F_1 \cup S_1$$. 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 $$G_2 = G_1 \cup S_2$$. 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 $$E_3 = E_2 \cup S_3$$. Given that $$E_1 = E_3$$, let p be the conditional probability of the event $$S_1 = \left\{1, 2 \right\}$$. Then the value of p is