Higher June 2019 Unit 2 Q17
17. A raffle is held at a school fair and a total of 100 tickets are sold.
Angharad buys three of the tickets and Meirion buys one ticket.
Tickets are selected at random and not replaced.
The first prize to be awarded is a calculator.
The second prize to be awarded is a voucher.
No other prizes are awarded.
(a) Calculate the probability that Angharad wins the calculator and Meirion wins the voucher. [2]
(b) Calculate the probability that no one wins a prize apart from Angharad or Meirion. [3]
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{3}{100} \times \dfrac{1}{99}\) | M1 | |
| \(= \dfrac{3}{9900} \left(=\dfrac{1}{3300}\right)\) ISW | A1 | Allow 3(.03…)×10-4 OR 0.0003(03…) or equivalent. A0 for 0.0003(03…)%. An unsupported 0.000303(…) gains M1A1. An unsupported 3/10000 OR 0.0003 gains no marks. |
| Scheme | Marks | Comments |
|---|---|---|
| \(2 \times \dfrac{3}{100} \times \dfrac{1}{99} \left(=\dfrac{6}{9900}=\dfrac{1}{1650}\right)\) \(+\, \dfrac{3}{100} \times \dfrac{2}{99} \left(=\dfrac{6}{9900}=\dfrac{1}{1650}\right)\) OR \(\dfrac{4}{100} \times \dfrac{3}{99}\) | M2 | M1 for sight of \(\left(\dfrac{3}{100}\times\dfrac{1}{99}\right) + \left(\dfrac{3}{100}\times\dfrac{1}{99}\right)\) OR \(\left(\dfrac{3}{100}\times\dfrac{1}{99}\right) + \left(\dfrac{1}{100}\times\dfrac{3}{99}\right)\) OR \(2 \times \dfrac{3}{100} \times \dfrac{1}{99}\) OR \(\left(\dfrac{3}{100}\times\dfrac{1}{99}\right) + \left(\dfrac{3}{100}\times\dfrac{2}{99}\right)\) |
| \(= \dfrac{12}{9900} \left(=\dfrac{1}{825}\right)\) ISW | A1 | Allow 1(.21…)×10-3 OR 0.001(21…) or equivalent. An unsupported answer of 0.00121(2…) gains M2A1. A0 for 0.001(21…)%. SC1 for working with replacement leading to an answer of 12/10000 (3/2500) OR 0.001(2) [may be unsupported]. |
17.(b) Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| \(1 - \left[\left(\dfrac{96}{100}\times\dfrac{95}{99}\right) + \left(2 \times \dfrac{3}{100}\times\dfrac{96}{99}\right) + \left(2 \times \dfrac{1}{100}\times\dfrac{96}{99}\right)\right]\) | M2 | M1 for sight of: \(\left[\left(\dfrac{96}{100}\times\dfrac{95}{99}\right) + \left(2 \times \dfrac{3}{100}\times\dfrac{96}{99}\right) + \left(2 \times \dfrac{1}{100}\times\dfrac{96}{99}\right)\right]\) OR \(1 - \left[\left(\dfrac{96}{100}\times\dfrac{95}{99}\right) + \left(\dfrac{3}{100}\times\dfrac{96}{99}\right) + \left(\dfrac{1}{100}\times\dfrac{96}{99}\right)\right]\) |
| \(= \dfrac{12}{9900} \left(=\dfrac{1}{825}\right)\) ISW | A1 | Allow 1(.21…)×10-3 OR 0.001(21…) or equivalent. An unsupported answer of 0.00121(2…) gains M2A1. A0 for 0.001(21…)%. SC1 for working with replacement leading to an answer of 12/10000 (3/2500) OR 0.001(2) [may be unsupported]. |