A fair die is rolled. Let the random variable X denote the number that falls bottommost on the die. Find the probability distribution of X.
A) $\begin{array} { l }
x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x )& \frac { 1 } { 12 } & \frac { 1 } { 6 } &\frac { 1 } { 4 }& \frac { 1 } { 4 } &\frac { 1 } { 6} &\frac { 1 } { 12 } \
\end{array}$
B) $\begin{array} { l }

x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x ) &\frac { 1 } { 12 } &\frac { 1 } { 12 }& \frac { 1 } { 3 } & \frac { 1 } { 6 } & \frac { 1 } { 12 } & \frac { 1 } { 12 } \
\end{array}$

C) $\begin{array} { l }

x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x ) &\frac { 1 } { 6 } &\frac { 1 } { 6 }& \frac { 1 } { 6 } & \frac { 1 } { 6 } & \frac { 1 } { 6} & \frac { 1 } { 6 } \
\end{array}$

D) $\begin{array} { l }
x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x ) &\frac { 1 } { 12 } &\frac { 1 } { 12 } & \frac{ 1 } { 12 } &\frac { 1 } { 12 } & \frac { 1 } { 12 } & \frac { 1 } { 12 } \
\end{array}$

E) $\begin{array} { l }
x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x ) &\frac { 1 } { 3 } &\frac { 1 } { 3 } & \frac{ 1 } { 3 } &\frac { 1 } {3} & \frac { 1 } { 3 } & \frac { 1 } { 3 } \
\end{array}$

Question

A fair die is rolled. Let the random variable X denote the number that falls bottommost on the die. Find the probability distribution of X.  
A) $\begin{array} { l } 
x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x )& \frac { 1 } { 12 } & \frac { 1 } { 6 } &\frac { 1 } { 4 }& \frac { 1 } { 4 } &\frac { 1 } { 6} &\frac { 1 } { 12 } \
\end{array}$  
B)   $\begin{array} { l }

x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x ) &\frac { 1 } { 12 } &\frac { 1 } { 12 }& \frac { 1 } { 3 } & \frac { 1 } { 6 } & \frac { 1 } { 12 } & \frac { 1 } { 12 } \
\end{array}$
 
C)   $\begin{array} { l }

x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x ) &\frac { 1 } { 6 } &\frac { 1 } { 6 }& \frac { 1 } { 6 } & \frac { 1 } { 6 } & \frac { 1 } { 6} & \frac { 1 } { 6 } \
\end{array}$
 
D)   $\begin{array} { l } 
x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x ) &\frac { 1 } { 12 } &\frac { 1 } { 12 } & \frac{ 1 } { 12 } &\frac { 1 } { 12 } & \frac { 1 } { 12 } & \frac { 1 } { 12 } \
\end{array}$
 
E)   $\begin{array} { l } 
x & 1 & 2 & 3 & 4 & 5 & 6\
P ( X = x ) &\frac { 1 } { 3 } &\frac { 1 } { 3 } & \frac{ 1 } { 3 } &\frac { 1 } {3} & \frac { 1 } { 3 } & \frac { 1 } { 3 } \
\end{array}$

Quizplus · Accepted Answer

Each face of a fair die has an equal probability of landing bottommost, making the probability for each outcome $1/6$.

A Fair Die Is Rolled B) C) D) E)