A discrete random variable $X$ can take values $0,1,2,3,4,5,6,7$ and its probability mass function is $$\mathrm { P } ( X = x ) = \left\{ \begin{array} { l l } c , & x = 0,1,2 \\ 2 c , & x = 3,4,5 \\ 5 c ^ { 2 } , & x = 6,7 \end{array} \quad ( \text { where } c \text { is a positive number } ) \right.$$ Let $A$ be the event that the random variable $X$ is at least 6, and let $B$ be the event that the random variable $X$ is at least 3. What is the value of $\mathrm { P } ( A \mid B )$? [3 points] (1) $\frac { 1 } { 5 }$ (2) $\frac { 1 } { 6 }$ (3) $\frac { 1 } { 7 }$ (4) $\frac { 1 } { 8 }$ (5) $\frac { 1 } { 9 }$
A discrete random variable $X$ can take values $0,1,2,3,4,5,6,7$ and its probability mass function is
$$\mathrm { P } ( X = x ) = \left\{ \begin{array} { l l } c , & x = 0,1,2 \\ 2 c , & x = 3,4,5 \\ 5 c ^ { 2 } , & x = 6,7 \end{array} \quad ( \text { where } c \text { is a positive number } ) \right.$$
Let $A$ be the event that the random variable $X$ is at least 6, and let $B$ be the event that the random variable $X$ is at least 3. What is the value of $\mathrm { P } ( A \mid B )$? [3 points]\\
(1) $\frac { 1 } { 5 }$\\
(2) $\frac { 1 } { 6 }$\\
(3) $\frac { 1 } { 7 }$\\
(4) $\frac { 1 } { 8 }$\\
(5) $\frac { 1 } { 9 }$