Question

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

Answer 1

Answer:

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