Let \(C_1\) and \(C_2\) be two biased coins such that the probabilities of getting head in a single toss are \(\frac{2}{…

Let \(C_1\) and \(C_2\) be two biased coins such that the probabilities of getting head in a single toss are \(\frac{2}{3}\) and \(\frac{1}{3}\), respectively. Suppose \(\alpha\) is the number of heads that appear when \(\mathrm{C}_1\) is tossed twice, independently, and suppose \(\beta\) is the number of heads that appear when \(\mathrm{C}_2\) is tossed twice, independently, Then the probability that the roots of the quadratic polynomial \(x^2-\alpha x+\beta\) are real and equal, is

[JEE Advanced 2020]