Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
James has a fair coin and a fair tetrahedral die with four faces labelled $1$, $2$, $3$, $4$. He tosses the coin one time and throws the die twice. The random variable $X$ is defined like this: if the coin lands heads, then $X$ is the total of the scores from the two die throws; if the coin lands tails, then $X$ is just the score from the first die throw.
(i)[2]
Explain that $X = 1$ is possible only when a tail is thrown, and hence show that $P(X = 1) = \frac{1}{8}$.
(ii)[4]
Show that $P(X = 3) = \frac{3}{16}$.
(iii)[3]
Copy the probability distribution table for $X$ and complete it.
(iv)[2]
Determine whether events $Q$ and $R$ are exclusive, and justify your response.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “If $H$ is thrown, the least score possible is $2$” …