A urn contains `5` white, `7` red and `8` black balls. If four balls are drawn one by one with replacement, what is the probability that
(i) all are white?  
(ii) only `3` are white?
(iii) none is white?
(iv) at last three are white?

Explanation

i) Total number of balls

`=5+7+8=20`

Number of white balls `=5`

Probability of getting white ball is one chance `=frac{5}{20}=frac{1}{4}`

All events are independent

Required probability `=frac{1}{4} times frac{1}{4} times frac{1}{4} times frac{1}{4} =(frac{1}{4})^4`


(ii) Probability of drawing white ball first time

`=^3C_1 frac{1}{4} times frac{1}{4} times frac{1}{4} =3 times (frac{1}{4})^3`


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