Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
During the school holidays, on any day Khalid either cycles with probability $0.6$, or rides his skateboard with probability $0.4$. He never does both on the same day. If he cycles, the probability that he hurts himself is $0.05$. If he uses his skateboard, the probability that he hurts himself is $0.75$.
(i)[2]
Determine the probability that Khalid hurts himself on a given day.
(ii)[2]
Given that Khalid hurts himself on a particular day, determine the probability that he is on his skateboard.
(iii)[2]
There are $45$ days of school holidays. Show that the variance of the number of days Khalid rides on his skateboard is equal to the variance of the number of days that Khalid rides on his bicycle.
(iv)[3]
Find the probability that Khalid rides on his skateboard on at least $2$ of $10$ randomly selected days during the school holidays.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write $P(H)=0.6\times0.05+0.4\times0.75$” …