A bag contains `3` red and `4` black balls. One ball is drawn and then replaced in the bag and the process is repeated. Every time the ball drawn is red we say that the draw has resulted in success. Let X be the number of successes in `3` draws. Assuming that at each draw each ball is equally likely to be selected, find the probability distribution of `X`.

Explanation

`P(X=0)=frac{4 times 4 times 4}{7 times 7 times 7}=frac{64}{343}`

`P(X=1)=frac{C_1^3 times 3 times 4 times 4}{7 times 7 times 7}=frac{144}{343}`

`P(X=2)=frac{C_2^3 times 3 times 3 times 4}{7 times 7 times 7}=frac{108}{343}`

`P(X=3)=frac{3 times 3 times 3}{7 times 7 times 7}=frac{27}{343}`