A bag contains 7 green, 4 white and 5 red balls. If four balls are drawn one by one with replacement, what is the probability that one is red?

Explanation

Let ` X ` denote the number of red balls drawn from `16` balls with replacement.
` X` follows a binomial distribution with` n=4,`

`p=frac{5}{16}, q=1-p=frac{11}{16}`

`P(X=r)=^{4} C_{r}(frac{5}{16})^{16}(frac{11}{16})^{4-r}`

`P(` One ball is red )`=P(X=1)`

`=^{4} C_{1}(frac{5}{16})^{1}(frac{11}{16})^{4-1}`

`=4(frac{5}{16})(frac{11}{16})^{3}`

`=frac{5}{4}(frac{11}{16})^{3}`