Question

From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.

Answer 1

let `x` be the event of defective bulb found
`p(x=0) = 4/5*4/5*4/5*4/5 =256/625`
`p(x=1) = .^4C_1(1/5)(4/5)^3 = 256/625`
`p(x=2) = .^4C_2(1/5)^2(4/5)^2 = 96/625`
`p(x=3) = .^4C_3(1/5)^3(4/5) = 16/625`
`p(x=4) = .^4C_4(1/5)^4 = 1/625`
answer