discussion7

Discussion 7 # 5.1.38

38 A manufactured lot of buggy whips has 20 items, of which 5 are defective. A random sample of 5 items is chosen to be inspected. Find the probability that the sample contains exactly one defective item

(a) if the sampling is done with replacement.

X <- 5
Y <- 1
Z <- factorial(X)/(factorial(Y)*factorial(X-Y))

P1 <- Z * (5/20)^1 *(15/20)^4
P1

## [1] 0.3955078

(b) if the sampling is done without replacement

# sampling is done without replacement
X1 <- 20-5
Y1 <- 5-1
Z1 <- factorial(X1)/(factorial(Y1)*factorial(X1-Y1))

X2 <- 20
Y2 <- 5
Z2 <- factorial(X2)/(factorial(Y2)*factorial(X2-Y2))

P2 <- Z * Z1 / Z2
P2

## [1] 0.440209