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.

(Plzz.. DON’T USE “Bernoulli trial and Binomial Distribution method”)

Find your answer inthe image. I have shown way of doing, you have to do the calculations.

Hello student,
Let X be the number of defective bulbs, so X = 0,1, 2, 3, 4.
here p = 1/5 and q = 4/5
P(X = 0) = 4C₀p^₀q⁴ = (24/30)⁴ = 256/625
P(X = 1) = 4C₁p¹q³ = 4.1/5 . (4/5)³ = 256/625
P(X = 2) = 4C₂p²q² = 4.(1/5)² . (4/5)² = 96/625
P(X = 3) = 4C₃p³q¹ = 4.(1/5)³ . (4/5)¹ = 16/625
P(X = 4) = 4C₄p⁴q⁰ = 4.(1/5)⁴ . (4/5)⁰ = 1/625
So, the probability distribution is
X 0 1 2 3 4
P(X) 256/625 256/625 96/625 16/625 1/625