| Date | November 2016 | Marks available | 5 | Reference code | 16N.2.sl.TZ0.7 |
| Level | SL only | Paper | 2 | Time zone | TZ0 |
| Command term | Find | Question number | 7 | Adapted from | N/A |
Question
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.
Let \(X\) be the number of red discs selected. Find the smallest value of \(m\) for which \({\text{Var}}(X{\text{ }}) < 0.6\).
Markscheme
\({\text{P(red)}} = \frac{5}{{15 + m}}\) 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]
