Let C1 and C2 be two biased coins such that the probabilities of getting heed in a single toss are 23 and 13, respectively. Suppose α is the number of heads that appear when C1 is tossed twice, independently, and suppose β is the number of heads that appear when C2 is tossed twice, independently. Then the probability that the roots of the quadratic polynomial x2−αx+β are real and equal, is

Let C1 and C2 be two biased coins such that the probabilities of getti

1.	Let C1 and C2 be two biased coins such that the probabilities of getting heed in a single toss are 23 and 13, respectively. Suppose α is the number of heads that appear when C1 is tossed twice, independently, and suppose β is the number of heads that appear when C2 is tossed twice, independently. Then the probability that the roots of the quadratic polynomial x2−αx+β are real and equal, is
Answer» Let $C_{1}$ and $C_{2}$ be two biased coins such that the probabilities of getting heed in a single toss are $\frac{2}{3}$ and $\frac{1}{3},$ respectively. Suppose $α$ is the number of heads that appear when $C_{1}$ is tossed twice, independently, and suppose $β$ is the number of heads that appear when $C_{2}$ is tossed twice, independently. Then the probability that the roots of the quadratic polynomial $x^{2} - α x + β$ are real and equal, is