Higher November 2022 Unit 1 Q18
18. Ffion has some blue cards and some yellow cards.
She takes 7 of the blue cards and 3 of the yellow cards and puts them in a box.
Ffion removes one card from the box at random and replaces it with two cards of the other colour.
Then she removes a second card from the box at random.
Calculate the probability that the two cards that Ffion removed are of different colours. [4]
| Scheme | Marks | Comments |
|---|---|---|
| Strategy P(blue, yellow) and P(yellow, blue) | S1 | Any indication e.g. tree diagram with relevant branches identified |
| 7/10 × 5/11 + 3/10 × 9/11 | M2 | M1 for sight of 7/10 × 5/11 or 3/10 × 9/11 OR M1 for a (consistent) error in a denominator within an otherwise complete calculation |
| = 62/110 (= 31/55) | A1 | ISW If M0 A0, award (S1) SC1 for an answer of 42/90 or 52/100 or 62/120 or equivalent (from non-replacement or replacing with one card only or replacing original card as well as additional cards.) |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| Strategy 1 – [P(blue, blue) + P(yellow, yellow)] | S1 | Any indication e.g. tree diagram with relevant branches identified |
| 1 – [7/10 × 6/11 + 3/10 × 2/11] | M2 | M1 for sight of 7/10 × 6/11 or 3/10 × 2/11 OR M1 for a (consistent) error in a denominator within an otherwise complete calculation |
| = 62/110 (= 31/55) | A1 | ISW If M0 A0, award (S1) SC1 for an answer of 42/90 or 52/100 or 62/120 or equivalent (from non-replacement or replacing with one card only or replacing original card as well as additional cards.) |