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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”)

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”)

Grade:12

2 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
6 years ago
Find your answer inthe image. I have shown way of doing, you have to do the calculations.228-1591_1.PNG
Latika Leekha
askIITians Faculty 165 Points
6 years ago
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) = 4C0p0q4 = (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

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