Higher November 2021 Paper 2 Q17
17 20 people were asked which device they used more often, laptop or phone.
The table shows the results.
| Laptop | Phone | |
|---|---|---|
| Male | 2 | 9 |
| Female | 4 | 5 |
(a) One male and one female are chosen at random.
Work out the probability that exactly one of them said laptop. [3 marks]
(b) Two males are chosen at random.
Work out the probability that they both said phone. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(\dfrac{2}{11}\) \(\times\) \(\dfrac{5}{9}\) or \(\dfrac{10}{99}\) or \(\dfrac{9}{11}\) \(\times\) \(\dfrac{4}{9}\) or \(\dfrac{36}{99}\) | M1 | oe fractions, decimals or percentages |
| \(\dfrac{2}{11}\) \(\times\) \(\dfrac{5}{9}\) \(+\) \(\dfrac{9}{11}\) \(\times\) \(\dfrac{4}{9}\) or \(\dfrac{10}{99}\) \(+\) \(\dfrac{36}{99}\) | M1dep | oe fractions, decimals or percentages |
| \(\dfrac{46}{99}\) | A1 | oe fraction, decimal or percentage allow 0.465 or better allow 46.5% or better SC2 \(\dfrac{54}{99}\) oe |
| Alternative method 2 | ||
| \(\dfrac{2}{11}\) \(\times\) \(\dfrac{4}{9}\) or \(\dfrac{8}{99}\) or \(\dfrac{9}{11}\) \(\times\) \(\dfrac{5}{9}\) or \(\dfrac{45}{99}\) | M1 | oe fractions, decimals or percentages |
| \(1 -\) \(\dfrac{2}{11}\) \(\times\) \(\dfrac{4}{9}\) \(-\) \(\dfrac{9}{11}\) \(\times\) \(\dfrac{5}{9}\) or \(1 -\) \(\dfrac{8}{99}\) \(-\) \(\dfrac{45}{99}\) or \(1 -\) \(\dfrac{53}{99}\) | M1dep | oe fractions, decimals or percentages |
| \(\dfrac{46}{99}\) | A1 | oe fraction, decimal or percentage allow 0.465 or better allow 46.5% or better SC2 \(\dfrac{54}{99}\) oe |
Additional guidance
| For M marks, accept values given as recurring decimals or correctly rounded to 2 dp or better eg Alt 1 \(0.18 \times 0.56 + 0.818 \times 0.44\) | M1M1 |
| M1 may be awarded for correct work, with no or incorrect answer, even if this is seen amongst multiple attempts | |
| Ignore conversion attempt if correct answer seen |
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{9}{11}\) \(\times\) \(\dfrac{8}{10}\) | M1 | oe fractions, decimals or percentages |
| \(\dfrac{72}{110}\) or \(\dfrac{36}{55}\) | A1 | oe fraction, decimal or percentage allow [0.65, 0.655] allow [65%, 65.5%] |
Additional guidance
| For M1, accept \(\dfrac{9}{11}\) given as a recurring decimal or correctly rounded to 2 dp or better eg \(0.82 \times 0.8\) | M1 |
| Ignore conversion attempt after correct answer seen |