Give the Probability Distribution for the Indicated Random Variable $\begin{array} { l } x & 1 & 2 & 3 \\P ( X = x ) &\frac { 1 } { 6 } &\frac { 2 } { 3 } & \frac{ 1 } { 6 } \\\end{array}$

Multiple Choice

Give the probability distribution for the indicated random variable.
A fair coin is tossed three times, and we count the number of "runs" that occur. A "run" is defined as a sequence of one or more of the same letter (e.g., HTH is 3 runs, TTH is 2 runs, and TTT is 1 run) .

A) $\begin{array} { l } x & 1 & 2 & 3 \\P ( X = x ) &\frac { 1 } { 6 } &\frac { 2 } { 3 } & \frac{ 1 } { 6 } \\\end{array}$
B) $\begin{array} { l } x & 1 & 2 & 3 \\P ( X = x ) &\frac { 1 } { 3 } &\frac { 1 } { 3 } & \frac{ 1 } {3 } \\\end{array}$

C) $\begin{array} { l } x & 1 & 2 & 3 \\P ( X = x ) &\frac { 1 } { 9 } &\frac { 7 } { 9 } & \frac{ 1 } { 9 } \\\end{array}$

D) $\begin{array} { l } x & 1 & 2 & 3 \\P ( X = x ) &\frac { 1 } {8 } &\frac { 3 } { 4 } & \frac{ 1 } { 8 } \\\end{array}$

E) $\begin{array} { l } x & 1 & 2 & 3 \\P ( X = x ) &\frac { 1 } { 4 } &\frac { 1 } { 2 } & \frac{ 1 } { 4 } \\\end{array}$