16N.2.SL.TZ0.S_7

pestleMathematicsAISLPaper 216N· sl-4-7-discrete-random-variablessource ↗

A jar contains 5 red discs, 10 blue discs and $m$ green discs. A disc is selected at random and replaced. This process is performed four times.

Write down the probability that the first disc selected is red.

[1]

Let $X$ be the number of red discs selected. Find the smallest value of $m$ for which ${\text{Var}}(X{\text{ }}) < 0.6$ .

[5]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

${\text{P(red)}} = \frac{5}{{15 + m}}$ A1 N1

[1 mark]

recognizing binomial distribution (M1)

eg $\,\,\,\,\,$ $X \sim B(n,{\text{ }}p)$

correct value for the complement of their $p$ (seen anywhere) A1

eg $\,\,\,\,\,$ $1 - \frac{5}{{15 + m}},{\text{ }}\frac{{10 + m}}{{15 + m}}$

correct substitution into ${\text{Var}}(X) = np(1 - p)$ (A1)

eg $\,\,\,\,\,$ $4\left( {\frac{5}{{15 + m}}} \right)\left( {\frac{{10 + m}}{{15 + m}}} \right),{\text{ }}\frac{{20(10 + m)}}{{{{(15 + m)}^2}}} < 0.6$

$m > 12.2075$ (A1)

$m = 13$ A1 N3

[5 marks]

Examiners’ report

[N/A]