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

Let $X=$ the number of income-tax turns with illegitimate deductions: $X\sim Bin(n, p).$

Given $n=5, p=6/12=0.5, q=1-p=1-0.5=0.5.$

$$P(X=3)=\dbinom{5}{3}(0.5)^3(0.5)^{5-3}=0.3125$$

The probability that the income-tax official will catch 3 income-tax turns with illegitimate deductions is 0.3125.