JEE Main 2021 — Probability Question with Solution

Given, set P = {1, 2, 3, 4, 5}

Let the two subsets be A and B

Then, n (A $$\cap$$ B) = 2 (as given in question)

We can choose two elements from set P in ⁵C₂ ways.

After choosing two common elements for set A and B, each of remaining three elements from set P have three choice (1) It can go to set A (2) It can go to set B (3) It don't go to any sets it stays at set P.

$$\therefore$$ Total ways for the three elements = 3 $$\times$$ 3 $$\times$$ 3 = 3³

$$\therefore$$ Required probability = $$\frac{{}^5{C}_2\times 3^3}{\left(2^5\right)\left(2^5\right)}$$ = $$\frac{{}^5{C}_2\times 3^3}{4^5}=\frac{10\times 27}{2^{10}}=\frac{135}{2^9}$$