$A$ bag contains $4$ red and $3$ black balls. One ball is drawn and then replaced in the bag and the process is repeated. Let $X$ denote the number of times a black ball is drawn in $3$ draws. Assuming that at each draw each ball is equally likely to be selected,the probability distribution of $X$ is given by:

• A

  $X$	$0$	$1$	$2$	$3$
  $P(X)$	$(\frac{4}{7})^3$	$\frac{9}{7} \times (\frac{4}{7})^2$	$\frac{12}{7} \times (\frac{3}{7})^2$	$(\frac{3}{7})^3$

• B

  $X$	$0$	$1$	$2$	$3$
  $P(X)$	$(\frac{3}{7})^3$	$\frac{12}{7} \times (\frac{3}{7})^2$	$\frac{9}{7} \times (\frac{4}{7})^2$	$(\frac{4}{7})^3$

• C

  $X$	$0$	$1$	$2$	$3$
  $P(X)$	$(\frac{3}{7})^3$	$\frac{9}{7} \times (\frac{4}{7})^2$	$\frac{12}{7} \times (\frac{3}{7})^2$	$(\frac{4}{7})^3$

• D

  $X$	$0$	$1$	$2$	$3$
  $P(X)$	$(\frac{4}{7})^3$	$\frac{12}{7} \times (\frac{4}{7})^2$	$\frac{9}{7} \times (\frac{3}{7})^2$	$(\frac{3}{7})^3$