Higher June 2017 Unit 1 Q17
17. A bag contains 6 red blocks, 4 green blocks and 2 yellow blocks.
Three blocks are taken from the bag, at random, without replacement.
(a) What is the probability that the first block removed is red, the second is green and the third is yellow? [2]
(b) Calculate the probability that all three blocks will be the same colour. [3]
(c) Write down the probability that the three blocks will not be the same colour. [1]
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{6}{12} \times \dfrac{4}{11} \times \dfrac{2}{10}\) | M1 | |
| \(= \dfrac{48}{1320}\) or equivalent (2/55) ISW | A1 | SC1 for 48/1728 or equivalent (1/36) (With replacement) |
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{6}{12} \times \dfrac{5}{11} \times \dfrac{4}{10} \;+\; \dfrac{4}{12} \times \dfrac{3}{11} \times \dfrac{2}{10}\) | M2 | F.T. consistent use of incorrect total from part (a). If a product is included for P(YYY), it must be worth zero in order for M2 to be awarded. M1 for either of the two (non-zero) terms or for a sum of 2 correct products and 1 incorrect. |
| \(= \dfrac{144}{1320}\) or equivalent (6/55) ISW | A1 | C.A.O. SC1 for 288/1728 or equivalent (1/6) (With replacement) |
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{1176}{1320}\) or equivalent (49/55) ISW | B1 | F.T. 1 – ‘their 144/1320’. |