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) = ⁿC_x

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) = ⁿC_x

P(0) = ⁴C₀ =

P(1) = ⁴C₁ =

P(2) = ⁴C₂ =

P(3) = ⁴C₃ =

P(4) = ⁴C₄ =

The probability distribution table is as follows,