| Date | May 2010 | Marks available | 2 | Reference code | 10M.2.sl.TZ2.3 |
| Level | SL only | Paper | 2 | Time zone | TZ2 |
| Command term | Find | Question number | 3 | Adapted from | N/A |
Question
Jan plays a game where she tosses two fair six-sided dice. She wins a prize if the sum of her scores is 5.
Jan tosses the two dice once. Find the probability that she wins a prize.
Jan tosses the two dice 8 times. Find the probability that she wins 3 prizes.
Markscheme
36 outcomes (seen anywhere, even in denominator) (A1)
valid approach of listing ways to get sum of 5, showing at least two pairs (M1)
e.g. (1, 4)(2, 3), (1, 4)(4, 1), (1, 4)(4, 1), (2, 3)(3, 2) , lattice diagram
\({\rm{P(prize)}} = \frac{4}{{36}}\) \(\left( { = \frac{1}{9}} \right)\) A1 N3
[3 marks]
recognizing binomial probability (M1)
e.g. \({\rm{B}}\left( {8,\frac{1}{9}} \right)\) , binomial pdf, \(\left( {\begin{array}{*{20}{c}}
8\\
3
\end{array}} \right){\left( {\frac{1}{9}} \right)^3}{\left( {\frac{8}{9}} \right)^5}\)
\({\text{P(3 prizes)}} = 0.0426\) A1 N2
[2 marks]
Examiners report
While many candidates were successful at part (a), far fewer recognized the binomial distribution in the second part of the problem.
While many candidates were successful at part (a), far fewer recognized the binomial distribution in the second part of the problem.
Those who did not obtain the correct answer at part (a) often scored partial credit by either drawing a table to represent the sample space or by noting relevant pairs.
