DSE 2010 Question 50: Probability and Bayes' theorem

Setup, from Q48 of the paper:

The number of loaves of bread sold by a bakery in a day is a random variable $X$ with density $f(x)=kx$ for $x\in[0,5)$, $f(x)=k(10-x)$ for $x\in[5,10)$, and $0$ for $x\ge 10$. As $f$ is a probability density function, the value of $k$ must be

(Same bakery density.) Events $A$ ($X\ge 5$) and $B$ ($X\in[3,8]$) are