Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
A fair tetrahedral die has four triangular faces, numbered $1$, $2$, $3$ and $4$. The result of a throw is the number shown on the face that comes to rest. The die is rolled three times. The random variable $X$ is the total of the three results.
(i)[3]
Show that $P(X = 9) = \frac{10}{64}$.
(ii)[3]
Copy and complete the probability distribution table for $X$.
(iii)[5]
Event $R$ is ‘the sum of the three scores is $9$’. Event $S$ is ‘the product of the three scores is $16$’. Determine whether events $R$ and $S$ are independent, showing your working.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Giving at least two valid outcome arrangements” …