Two continuous random variables $X$ and $Y$ have ranges $0 \leq X \leq 6$ and $0 \leq Y \leq 6$, with probability density functions $f ( x )$ and $g ( x )$ respectively. The graph of the probability density function $f ( x )$ of random variable $X$ is shown in the figure. For all $x$ with $0 \leq x \leq 6$, $$f ( x ) + g ( x ) = k \text{ (where } k \text{ is a constant)}$$ When $\mathrm { P } ( 6 k \leq Y \leq 15 k ) = \frac { q } { p }$, find the value of $p + q$. (Here, $p$ and $q$ are coprime natural numbers.) [4 points]
Two continuous random variables $X$ and $Y$ have ranges $0 \leq X \leq 6$ and $0 \leq Y \leq 6$, with probability density functions $f ( x )$ and $g ( x )$ respectively. The graph of the probability density function $f ( x )$ of random variable $X$ is shown in the figure.
For all $x$ with $0 \leq x \leq 6$,
$$f ( x ) + g ( x ) = k \text{ (where } k \text{ is a constant)}$$
When $\mathrm { P } ( 6 k \leq Y \leq 15 k ) = \frac { q } { p }$, find the value of $p + q$. (Here, $p$ and $q$ are coprime natural numbers.) [4 points]