(i)[2]
Show that the value of $x$ is $0.225$.
(ii)[3]
If it is given that Benju is not late for work, find the probability that he chooses the hilly route.
Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
Benju rides to work every morning and has two routes from which to choose. He takes the hilly route with probability $0.4$ and the busy route with probability $0.6$. If he goes by the hilly route, the probability that he is late for work is $x$, and if he goes by the busy route, the probability that he is late for work is $2x$. The probability that Benju is late for work on any day is $0.36$.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “A correct equation is formed, such as $0.4x+0.6(2x)=0.36$ or $0.4(1-x)+0.6(1-2x)=0.64$” …
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