Foundation June 2019 Unit 2 Q17
17. Alison and Sarfraz play a game. They each have a different bag of cards.
Alison has the following cards in her bag.
CAERNARFON
Sarfraz has the following cards in his bag.
ABER
They each take a card at random from their own bag. They make a note of the letter, and return the card to the bag.
They each do this 100 times.
Who do you think is likely to choose the letter R more often?
Alison ☐ Sarfraz ☐
You must explain your decision and show all your working. [4]
| Scheme | Marks | Comments |
|---|---|---|
| P(Alison chooses letter R) = 2/10 or equivalent. | B1 | B1 for sight of 2/10 if unambiguously for Alison. |
| P(Sarfraz chooses letter R) = ¼ or equivalent. | B1 | B1 for sight of 1/4 if unambiguously for Sarfraz. As probability not asked for, allow e.g. ‘2 chances in 10’ and ‘one chance in four’. B1 marks may be implied in subsequent work. |
| Use of 2/10 × 100 OR ¼ × 100 | M1 | Calculation may be done in stages. |
| 20 AND 25 clearly implying that Sarfraz is the most likely to choose letter R | A1 | There is no requirement to tick the box as long as there is no contradiction. Do not accept, on its own, e.g. ‘Sarfraz has less letters to choose from’ for the A1. |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| P(Alison chooses letter R) = 2/10 or equivalent. | B1 | B1 for sight of 2/10 if unambiguously for Alison. |
| P(Sarfraz chooses letter R) = ¼ or equivalent. | B1 | B1 for sight of 1/4 if unambiguously for Sarfraz. As probability not asked for, allow e.g. ‘2 chances in 10’ and ‘one chance in four’ |
| Attempting to give probabilities in a common format. | M1 | |
| Correct common format e.g. 4/20 AND 5/20 or 0·2 AND 0·25 clearly implying that Sarfraz is the most likely to choose letter R | A1 | There is no requirement to tick the box as long as there is no contradiction. Do not accept, on its own, e.g. ‘Sarfraz has less letters to choose from’ for the A1. |