Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
Sanket takes part in a game with a biased die, where an even result is twice as likely as an odd result. The three even faces all have the same probability, and the three odd faces all have the same probability.
(i)[2]
Find the probability of throwing an odd number with this die.
(ii)[2]
Show that $P(X = 8) = \frac{2}{9}$.
(iii)[2]
Given that $\text{E}(X) = \frac{58}{9}$, determine $\mathrm{Var}(X)$.
(iv)[2]
Find the probability that the sum of the two scores is 16.
(v)[3]
Given that the total of the two throws is 16, find the probability that the first throw scored 6.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Probability work using $P(\text{even})=2y$ and total probability $=1$” …