(a)[2]
Show that the probability of Sadie taking exactly $1$ red ball is $\frac{15}{56}$.
(b)[3]
Construct the probability distribution table for $X$.
(c)[2]
Using the fact that $\text{E}(X) = \frac{15}{8}$, find $\mathrm{Var}(X)$.
Mathematics 9709 · AS & A Level · Discrete random variables
Discrete random variables — practice question
A bag has $5$ red balls and $3$ blue balls inside it. Sadie selects $3$ balls at random from the bag, without replacement. The random variable $X$ denotes the number of red balls that she selects.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies the correct probability structure, such as $\frac{5}{8}\times\frac{3}{7}\times\frac{2}{6}\times 3$ or an equivalent arrangement” …
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