20% of the bulbs produced by a machine are defective. Find the probability distribution of the number of defective bulbs in a sample of 4 bulbs chosen at random. [CBSE 2004C]
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,
