The mean and variance of a binomial distribution are 4 and 3 respectively, then the probability of getting exactly six successes in this distribution, is a. `\ ^(16)C_6(1/4)^(10)(3/4)^6` b. `\ ^(16)C_6(1/4)^6(3/4)^(10)` c. `\ ^(12)C_6(1/(20))^(\ )(3/4)^6` d. `\ ^(12)C_6(1/4)^6(3/4)^6`

Explanation

`\ ^{16} C_{6}(frac{1}{4})^{6}(frac{3}{4})^{10}`


Mean `(n p)=4` and Variance `(n p q)=3`


`therefore q=frac{3}{4} `

`Rightarrow p=1-frac{3}{4}=frac{1}{4} { and } n=16`


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