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) $\frac { 40 } { 81 }$ (B) $\frac { 20 } { 81 }$ (C) $\frac { 1 } { 2 }$ (D) $\frac { 1 } { 4 }$
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) $\frac { 40 } { 81 }$\\
(B) $\frac { 20 } { 81 }$\\
(C) $\frac { 1 } { 2 }$\\
(D) $\frac { 1 } { 4 }$