| Date | November 2010 | Marks available | 2 | Reference code | 10N.1.sl.TZ0.6 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 6 | Adapted from | N/A |
Question
A survey was carried out in a group of 200 people. They were asked whether they smoke or not. The collected information was organized in the following table.
One person from this group is chosen at random.
Write down the probability that this person is a smoker.
Write down the probability that this person is male given that they are a smoker.
Find the probability that this person is a smoker or is male.
Markscheme
\(\frac{{90}}{{200}}(0.45,{\text{ }}45{\text{ }}\% )\) (A1)(A1) (C2)
Note: Award (A1) for numerator, (A1) for denominator.
[2 marks]
\(\frac{{60}}{{90}}(0.\bar 6,{\text{ }}0.667,{\text{ }}66.\bar 6{\text{ }}\% ,{\text{ }}66.6 \ldots {\text{ }}\% ,{\text{ }}66.7{\text{ }}\% )\) (A1)(A1)(ft) (C2)
Notes: Award (A1) for numerator, (A1)(ft) for denominator, follow through from their numerator in part (a). Last mark is lost if answer is not a probability.
[2 marks]
\(\frac{{90}}{{200}} + \frac{{100}}{{200}} - \frac{{60}}{{200}}\) (M1)
Note: Award (M1) for correct substitution in the combined events formula. Follow through from their answer to part (a).
\( = \frac{{130}}{{200}}(0.65,{\text{ }}65{\text{ }}\% )\) (A1)(ft)
OR
\(\frac{{60}}{{200}} + \frac{{40}}{{200}} + \frac{{30}}{{200}}\) (M1)
Note: Award (M1) for adding the correct fractions.
\( = \frac{{130}}{{200}}(0.65,{\text{ }}65{\text{ }}\% )\) (A1)
OR
\(1 - \frac{{70}}{{200}}\) (M1)
Note: Award (M1) for subtraction of correct fraction from 1.
\( = \frac{{130}}{{200}}(0.65,{\text{ }}65{\text{ }}\% )\) (A1) (C2)
[2 marks]
Examiners report
This question was generally well answered by many of the candidates. Many found the conditional probability in part b) easier compared to previous sessions, since they were able to write it down directly from the table. A number of candidates found the final part difficult with a significant number unable to use the combined events probability formula correctly.
This question was generally well answered by many of the candidates. Many found the conditional probability in part b) easier compared to previous sessions, since they were able to write it down directly from the table. A number of candidates found the final part difficult with a significant number unable to use the combined events probability formula correctly.
This question was generally well answered by many of the candidates. Many found the conditional probability in part b) easier compared to previous sessions, since they were able to write it down directly from the table. A number of candidates found the final part difficult with a significant number unable to use the combined events probability formula correctly.
