Higher November 2023 Paper 5 Q25
25 Riley has a set of cards.
Each card has a triangle or circle drawn on it and is coloured red or blue.
The table gives some information about the number of each type of card.
| Number of cards with a triangle | Number of cards with a circle | |
|---|---|---|
| Number of blue cards | 3 | 8 |
| Number of red cards | 9 | 2 |
Riley chooses three of these cards at random without replacement.
All three of these cards have a circle drawn on them.
Riley says
| The probability that two of these three cards are blue and one is red is less than \(\frac{1}{2}\). |
Is Riley correct?
You must show your working. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Yes and \(\frac{336}{720}\) oe or better with correct working | 5 | M4 for \(3 \times \frac{8}{10} \times \frac{7}{9} \times \frac{2}{8}\) oe or M3 for \(k \times \frac{8}{10} \times \frac{7}{9} \times \frac{2}{8}\) oe or M2 for \(\frac{8}{10}\), \(\frac{7}{9}\) and \(\frac{2}{8}\) oe used or M1 for \(\frac{8}{10}\) oe seen or for three combinations soi BBR, BRB, RBB | “Correct working” requires M4 For 5 marks oe or better e.g. \(\frac{7}{15}\), \(\frac{21}{45}\), 0.467 or 0.4666.. where \(k\) = 1 or 2 |
| Alternative Method: M4 for \(3 \times \dfrac{\frac{8}{22} \times \frac{7}{21} \times \frac{2}{20}}{\frac{10}{22} \times \frac{9}{21} \times \frac{8}{20}}\) oe or M3 for \(k \times \dfrac{\frac{8}{22} \times \frac{7}{21} \times \frac{2}{20}}{\frac{10}{22} \times \frac{9}{21} \times \frac{8}{20}}\) oe or M2 for \(\frac{10}{22} \times \frac{9}{21} \times \frac{8}{20}\) oe or \(\frac{8}{22} \times \frac{7}{21} \times \frac{2}{20}\) oe or M1 for \(\frac{10}{22}\) oe seen or \(\frac{8}{22}\) oe seen | where \(k\) = 1 or 2 | ||
| If 0 or M1 scored, instead award SC2 for answer \(\frac{336}{720}\) oe (or better) with no or insufficient working If 0 scored, instead award SC1 for answer \(\frac{112}{720}\) or \(\frac{224}{720}\) oe (or better) with no or insufficient working | With replacement (apply similar to the alternative method): SC2 for \(3 \times \frac{8}{10} \times \frac{8}{10} \times \frac{2}{10}\) oe \(\left[\frac{48}{125}\right]\) or SC1 for \(k \times \frac{8}{10} \times \frac{8}{10} \times \frac{2}{10}\) oe (\(k\) = 1 or 2) Circle condition missed (apply similar to the alternative method): SC2 for \(3 \times \frac{11}{22} \times \frac{10}{21} \times \frac{11}{20}\) oe \(\left[\frac{11}{28}\right]\) or SC1 for \(k \times \frac{11}{22} \times \frac{10}{21} \times \frac{11}{20}\) oe (\(k\) = 1 or 2) | ||