Answer to Question #218320 in Statistics and Probability for rene

Question

Find the probability that the income-tax official will catch 3 income-tax turns with illegitimate

deductions. if he randomly selects 5 returns from among 12 returns of which 6 contain

illegitimate deductions

Answer 1

N=12

n=5

x=3

k=6

Hypergeometric distribution

$P(X) = \frac{\binom{k}{x} \binom{N-k}{n-x}}{\binom{N}{n}} \\ P(3) = \frac{\binom{6}{3} \binom{12-6}{5-3}}{\binom{12}{5}} \\ P(3) = \frac{120 \times 360}{3991680} \\ P(3) = 0.0108$