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

the probability that the obstetrician has delivered no child with polydactyly in her first 100 deliveries = 0.819

Step-by-step explanation:

This is a binomial distribution problem

Probability of a polydactyl case, p = 1/500 = 0.002

Probability of no polydactyl case, q = 1 - 0.002 = 0.998

Binomial distribution function is represented by

P (X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

For this case,

x = 0

n = 100

P (X = 0) = ¹⁰⁰C₀ (0.02) ⁰ (0.998) ¹⁰⁰⁻⁰

P (X = 0) = ¹⁰⁰C₀ (0.02) ⁰ (0.998) ¹⁰⁰

P (X = 0) = 1 * 1 * 0.819 = 0.819