Give the probability distribution for the indicated random variable.
A black and white die are rolled, and consider the following random variable.
$X = \left\{ \begin{array} { l }
0 , \text { if both numbers are odd } \
3 , \text { if one number is odd and one is even } \
6 , \text { if both numbers are even }
\end{array} \right.$
A) $\begin{array} { l }
x & 0 & 3& 6 \
P ( X = x ) &\frac { 1 } { 4 } &\frac { 1 } { 4 } & \frac{ 1 } { 2 } \
\end{array}$
B) $\begin{array} { l }
x & 0 & 3& 6 \
P ( X = x ) &\frac { 2 } { 3} &\frac { 1 } { 6 } & \frac{ 1 } { 6 } \
\end{array}$

C) $\begin{array} { l }
x & 0 & 3& 6 \
P ( X = x ) &\frac { 1 } { 3 } &\frac { 1 } { 3 } & \frac{ 1 } { 3 } \
\end{array}$
D) $\begin{array} { l }
x & 0 & 3& 6 \
P ( X = x ) &\frac { 1 } { 2 } &\frac { 1 } { 4 } & \frac{ 1 } { 4 } \
\end{array}$

E) $\begin{array} { l }
x & 0 & 3& 6 \
P ( X = x ) &\frac { 1 } { 4 } &\frac { 1 } {2 } & \frac{ 1 } { 4 } \
\end{array}$

Question

Give the probability distribution for the indicated random variable.  
A black and white die are rolled, and consider the following random variable.
  $X = \left\{ \begin{array} { l } 
0 , \text { if both numbers are odd } \
3 , \text { if one number is odd and one is even } \
6 , \text { if both numbers are even }
\end{array} \right.$  
A)  $\begin{array} { l } 
x & 0 & 3& 6 \
P ( X = x ) &\frac { 1 } { 4 } &\frac { 1 } { 4 } & \frac{ 1 } { 2 }  \
\end{array}$  
B)   $\begin{array} { l } 
x & 0 & 3& 6 \
P ( X = x ) &\frac { 2 } { 3} &\frac { 1 } { 6 } & \frac{ 1 } { 6 }  \
\end{array}$
 
C) $\begin{array} { l } 
x & 0 & 3& 6 \
P ( X = x ) &\frac { 1 } { 3 } &\frac { 1 } { 3 } & \frac{ 1 } { 3 }  \
\end{array}$  
D)   $\begin{array} { l } 
x & 0 & 3& 6 \
P ( X = x ) &\frac { 1 } { 2 } &\frac { 1 } { 4 } & \frac{ 1 } { 4 }  \
\end{array}$
 
E)   $\begin{array} { l } 
x & 0 & 3& 6 \
P ( X = x ) &\frac { 1 } { 4 } &\frac { 1 } {2 } & \frac{ 1 } { 4 }  \
\end{array}$

Quizplus · Accepted Answer

Each die has 3 odd (1, 3, 5) and 3 even (2, 4, 6) numbers. The probability of both odd is $(\frac{3}{6})^2 = \frac{1}{4}$, both even is also $(\frac{3}{6})^2 = \frac{1}{4}$, and one odd one even (or vice versa) is $2 \times \frac{3}{6} \times \frac{3}{6} = \frac{1}{2}$.

Give the Probability Distribution for the Indicated Random Variable A) x036P(X=x)141412\begin{array} { l } x & 0 & 3& 6 \\P ( X = x ) &\frac { 1 } { 4 } &\frac { 1 } { 4 } & \frac{ 1 } { 2 } \\\end{array}xP(X=x)​041​​341​​621​​

Give the Probability Distribution for the Indicated Random Variable A) $\begin{array} { l } x & 0 & 3& 6 \\P ( X = x ) &\frac { 1 } { 4 } &\frac { 1 } { 4 } & \frac{ 1 } { 2 } \\\end{array}$