There are 4 white and 5 red balls ina bag.Three balls are drawn with replacement. Find the probability distribution for number of red balls.

Answer

N/a

Explanation

Probability of drawing a red ball
`p=5/(5+4)=5/9`
Probability that ball drawn is not red
`q=1-p=1-5/9=4/9`
Now probability of getting no red ball
`P(X=0)=q.q.q`
`=4/9xx4/9xx4/9=64/729`
Probability of getting exactly one red ball
`P(X=1)=p.q.q+q.p.q+q.q.p`
`=5/9 . 4/9 . 4/9+4/9 . 5/9 . 4/9+4/9 . 4/9 . 5/9`
`=240/729`
Probability of getting two red balls
`P(X=2)p.p.q+p.q.p+q.p.p`
`=5/9 . 5/9 . 4/9+5/9 . 4/9 . 5/9 +4/9 . 5/9 . 5/9`
`=300/729`
Probability of getting three red balls
`P(X=3)=p.p.p=5/9 . 5/9 . 5/9=125/729`
Therefore the probability distribution is