SSC Steno Grade C and D 8 Aug 2025 Shift 3 Paper

Concept:Use Bayes' theorem to find the probability that the drawn coin is double-headed given that it showed heads three times.Explanation:Total coins = 8. Four are fair (one head, one tail) and four are double-headed.Probability of picking a fair coin = $\frac{4}{8} = \frac{1}{2}$.Probability of picking a double-headed coin = $\frac{4}{8} = \frac{1}{2}$.If the coin is fair, probability of three heads in a row = $(\frac{1}{2})^3 = \frac{1}{8}$.If the coin is double-headed, probability of three heads = $1$.Total probability of getting three heads = $(\frac{1}{2} \times 1) + (\frac{1}{2} \times \frac{1}{8}) = \frac{1}{2} + \frac{1}{16} = \frac{9}{16}$.Probability that the coin is double‑headed and gives three heads = $\frac{1}{2} \times 1 = \frac{1}{2}$.Required probability = $\frac{\frac{1}{2}}{\frac{9}{16}} = \frac{1}{2} \times \frac{16}{9} = \frac{8}{9}$.Answer:$\frac{8}{9}$ (Option B).