Answer :

Given : 20% of the bulbs produced by a machine are defective.


To find probability distribution of a number of defective bulbs in a sample of 4 bulbs chosen at random.


Formula used :


The probability distribution table is given by ,



Where P(x) = nCx


Here p is the probability of getting a defective bulb.


q = 1 – p


Let the total number of bulbs produced by a machine be x


20% of the bulbs produced by a machine are defective.


Number of defective bulbs produced by a machine = =


X denotes the number of defective bulbs in a sample of 4 bulbs chosen at random.


Let p be the probability of getting a defective bulb,


p = =


p =


q = 1 – p = 1 - =


q =


since 4 bulbs are chosen at random, n = 4


X can take the values of 0,1,2,3,4


P(x) = nCx


P(0) = 4C0 =


P(1) = 4C1 =


P(2) = 4C2 =


P(3) = 4C3 =


P(4) = 4C4 =


The probability distribution table is as follows,



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