Polydactyly is a fairly common congenital abnormality in which a baby is born with one or more extra fingers or toes. It is reported in about one child in every 500 . A young obstetrician celebrates her first 100 deliveries. What is the probability that the obstetrician has delivered no child with polydactyly? (Enter your answer rounded to four decimal places.)

Answer:the probability that the obstetrician has delivered no child with polydactyly in her first 100 deliveries = 0.819Step-by-step explanation:This is a binomial distribution problem Probability of a polydactyl case, p = 1/500 = 0.002Probability of no polydactyl case, q = 1 - 0.002 = 0.998Binomial distribution function is represented byP(X = x) = ⁿCₓ pˣ qⁿ⁻ˣFor this case,x = 0n = 100P(X = 0) = ¹⁰⁰C₀ (0.02)⁰ (0.998)¹⁰⁰⁻⁰P(X = 0) = ¹⁰⁰C₀ (0.02)⁰ (0.998)¹⁰⁰P(X = 0) = 1 × 1 × 0.819 = 0.819