Mathematics 9709 · AS & A Level · The Poisson distribution
The Poisson distribution — practice question
A box holds $6$ discs of the same size, with $4$ blue discs and $2$ red discs. The discs are drawn at random one at a time without replacement. Let $X$ denote the number of discs drawn up to and including the first blue disc.
(i)[2]
Show that $P(X = 3) = \frac{1}{15}$ using the information given.
(ii)[3]
Construct the probability distribution table for $X$.
(a(i))[2]
Show that $P(X = 3) = \frac{1}{15}$ by carrying out the calculation.
(a(ii))[3]
Construct a probability distribution table for $X$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “A correct probability expression for $P(X=3)$, for example $\frac{2}{6}\times\frac{1}{5}\times\frac{4}{4}$ or any equivalent valid form” …