Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
Rory owns $10$ cards. On four of them, a $3$ is shown, while the other six each show a $4$. He chooses three cards at random without replacement, then adds the numbers on those cards.
(a(i))[3]
Show that $P(\text{the sum of the numbers on the three cards is } 11) = \frac{1}{2}$.
(a(ii))[4]
Draw up a probability distribution table for the sum of the numbers on the three cards.
(a(iii))[3]
Event $R$ is ‘the sum of the numbers on the three cards is $11$’. Event $S$ is ‘the number on the first card taken is a $3$’. Determine whether events $R$ and $S$ are independent. Justify your answer.
(a(iv))[1]
Determine whether events $R$ and $S$ are exclusive. Justify your answer.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Looking at the selection $(3,4,4)$ and its permutations” …