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.

Answer

N/a

Explanation

Let `X` be a random variable.
For a sample of 4 bulbs,
Possibe values of `X=0,1,2,3,4` ltbrLgt Let `p=` probability of getting a defective bulb
`=6/30=1/5`
`:.q=1-p=1-1/5=4/5`
`P(X=0)=q.q.q.q=4/5 . 4/5 . 4/5 . 4/5=256/625`
Now `P(X=1)=p.q.q.q+q.p.q.q`
`+q.q.p.q+q.q.q.p`
`=4xx1/5xx4/5xx4/5xx4/5=256/625`
`P(X=2)=p.p.q.q+p.q.p.q`
`+p.q.q.p+q.p.p.q`
`+q.p.q.p+q.q.p.p`
`=6xx1/5xx1/5xx4/5xx4/5=96/625`
`P(X=3)=p.p.p.q+p.p.q.p`
`+p.q.p.p+q.p.p.p`
`=4xx1/5xx1/5xx1/5xx4/5=16/625`
`P(X=4)=p.p.p.p=1/5xx1/5xx1/5xx1/5=1/625`
Therefore, required probability distribution is: