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.


Given: A lot of 30 bulbs which include 6 defectives.

Then number of non-defective bulbs = 30 – 6 = 24


As 4 bulbs are drawn at random with replacement.


Let X denotes the number of defective bulbs from the selected bulbs.


Clearly, X can take the value of 0, 1, 2, 3 or 4.


P(X = 0) = P(4 are non defective and 0 defective)


P(X = 1) = P(3 are non defective and 1 defective)


P(X = 2) = P(2 are non defective and 2 defective)


P(X = 3) = P(1 are non defective and 3 defective)


P(X = 4) = P(0 are non defective and 4 defective)


Hence, the required probability distribution is,


X



0



1



2



3



4



P(X)













6
1