| Date | November 2012 | Marks available | 1 | Reference code | 12N.3sp.hl.TZ0.1 |
| Level | HL only | Paper | Paper 3 Statistics and probability | Time zone | TZ0 |
| Command term | State | Question number | 1 | Adapted from | N/A |
Question
Bill also has a box with 10 biscuits in it. 4 biscuits are chocolate and 6 are plain. Bill takes a biscuit from his box at random, looks at it and replaces it in the box. He repeats this process until he has looked at 5 biscuits in total. Let B be the number of chocolate biscuits that Bill takes and looks at.
State the distribution of B .
Find P(B = 3) .
Find P(B = 5) .
Markscheme
B has the binomial distribution \(\left( {B\left( {5,\frac{4}{{10}}} \right)} \right)\) A1
[1 mark]
\({\text{P}}(B = 3) = \left( {\left( {\begin{array}{*{20}{c}}
5 \\
3
\end{array}} \right){{\left( {\frac{4}{{10}}} \right)}^3}{{\left( {\frac{6}{{10}}} \right)}^2} = } \right)\frac{{144}}{{625}}( = 0.2304)\) (M1)A1
Note: Accept 0.230.
[2 marks]
\({\text{P}}(B = 5) = \left( {{{\left( {\frac{4}{{10}}} \right)}^5} = } \right)\frac{{32}}{{3125}}( = 0.01024)\) (M1)A1
Note: Accept 0.0102.
[2 marks]
Examiners report
This was generally well answered. Some students did not read the question carefully enough and see the comparisons made between the Hypergeometric distribution and the Binomial distribution, with 5 trials (some candidates went to 10 trials) in each case. Part (h) caused the most problems and it was very rare to see a script that gained the reasoning mark for saying that A and B were independent events. This question was a good indicator of the standard of the rest of the paper.
This was generally well answered. Some students did not read the question carefully enough and see the comparisons made between the Hypergeometric distribution and the Binomial distribution, with 5 trials (some candidates went to 10 trials) in each case. Part (h) caused the most problems and it was very rare to see a script that gained the reasoning mark for saying that A and B were independent events. This question was a good indicator of the standard of the rest of the paper.
This was generally well answered. Some students did not read the question carefully enough and see the comparisons made between the Hypergeometric distribution and the Binomial distribution, with 5 trials (some candidates went to 10 trials) in each case. Part (h) caused the most problems and it was very rare to see a script that gained the reasoning mark for saying that A and B were independent events. This question was a good indicator of the standard of the rest of the paper.
