QJEEAdv20Maa8cc: JEE Advanced 2020 Mathematics - Class 12 JEEAdv20Maa8cc Solution: Let C 1 and C 2 be two biased coins such that the probabilities …

It is given that $$\alpha$$ is the number of heads that appear when C₁ is tossed twice, the probability distribution of random variable $$\alpha$$ is



Similarly, it is given that $$\beta$$ is the number of heads that appear when C₂ is tossed twice, so probability distribution of random variable $$\beta$$ is



Now, as the roots of quadratic polynomial x² $$-$$ $$\alpha$$x + $$\beta$$ are real and equal, so D = $$\alpha$$² $$-$$ 4$$\beta$$ = 0 and it is possible if ($$\alpha$$, $$\beta$$) = (0, 0) or (2, 1)

$$\therefore$$ Required probability

= $${\left(\frac{1}{3}\right)}^2{\left(\frac{2}{3}\right)}^2+{\left(\frac{2}{3}\right)}^2\left(\frac{4}{9}\right)$$

= $$\frac{4}{81}$$ + $$\frac{16}{81}$$ = $$\frac{20}{81}$$