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 $C_1$ is tossed twice, independently, and suppose $\beta$ is the number of heads that appear when $C_2$ is tossed twice, independently. Then the probability that the roots of the quadratic polynomial $x^2-\alpha x+\beta$ are real and equal, is

• A

  $\frac{40}{81}$
• Correct answer
  B

  $\frac{20}{81}$
• C

  $\frac{1}{2}$
• D

  $\frac{1}{4}$

Hence, the correct answer is option: 'B'.