(i)[2]
Show that the value of $P(X = 2)$ is $\frac{2}{15}$.
(ii)[4]
Draw up a probability distribution table for $X$.
(iii)[3]
Given that $X = 3$, find the probability that the card selected from pack A is a $1$.
Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
Pack A contains ten cards labelled $0, 0, 1, 1, 1, 1, 1, 3, 3, 3$. Pack B contains six cards labelled $0, 0, 2, 2, 2, 2$. One card is drawn at random from each pack. The random variable $X$ is the total of the two card numbers.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct approach: multiply the probabilities, e.g. $\frac{2}{10}\times\frac{4}{6}$” …
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