A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails.

Question

$\begin{array}{1 1} \begin{matrix} \textbf{X} & 0 &1 &2 \\ \textbf{P(X)} &\large \frac{9}{16} &\large \frac{3}{8} &\large\frac{1}{16}\end{matrix} \\ \begin{matrix} \textbf{X} & 0 &1 &2 \\ \textbf{P(X)} &\large \frac{9}{16} &\large \frac{5}{8} &\large\frac{1}{16}\end{matrix} \\ \begin{matrix} \textbf{X} & 0 &1 &2 \\ \textbf{P(X)} &\large \frac{1}{16} &\large \frac{3}{8} &\large\frac{9}{16}\end{matrix} \\ \begin{matrix} \textbf{X} & 0 &1 &2 \\ \textbf{P(X)} &\large \frac{1}{16} &\large \frac{5}{8} &\large\frac{1}{16}\end{matrix}\end{array}$