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) = \(n_{C_x}p^xq^{n-x}\)
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 \(=\frac{20}{100}\times (\chi)=\frac{x}{5}\)
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,
since 4 bulbs are chosen at random, n = 4
X can take the values of 0,1, 2, 3, 4
The probability distribution table is as follows,
