Higher June 2019 Unit 1 Q18
18. A box contains 4 yellow cards and 6 red cards.
Three cards are chosen at random, one at a time, without replacement.
(a) Calculate the probability that the first two cards are yellow and the third card is red.
You must show all your working. [2]
You must show all your working. [2]
(b) Calculate the probability that at least one yellow card is chosen. [3]
| Scheme | Marks | Comments |
|---|---|---|
| 4/10 × 3/9 × 6/8 or equivalent | M1 | Accept e.g. 6/10 × 4/9 × 3/8 or (6 × 4 × 3)/(10 × 9 × 8) |
| 72/720 (= 1/10) or equivalent | A1 | ISW |
| Scheme | Marks | Comments |
|---|---|---|
| 1 – P(three red) or 1 – P(no yellow) | S1 | May be implied by subsequent working. |
| = 1 – [6/10 × 5/9 × 4/8] (= 1 – 120/720 or 1 – 1/6) | M1 | Complete method. |
| = 600/720 (= 5/6) or equivalent | A1 | ISW FT from part (a) consistent use of a wrongly calculated denominator. If no other marks awarded, SC1 for sight of 784/1000 or equivalent (from a method ‘with replacement’) |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| P(YRR or RYR or RRY or YYR or YRY or RYY or YYY) or equivalent (allow up to two of these terms to be missing or incorrect for this mark) | S1 | |
| = 4/10×6/9×5/8×3 + 4/10×3/9×6/8×3 + 4/10×3/9×2/8 or equivalent (complete method required for this mark) | M1 | FT 4/10×6/9×5/8×3 + ‘their part (a)’ × 3 + 4/10×3/9×2/8 |
| = 600/720 (= 5/6) or equivalent ISW | A1 |