Higher November 2022 Unit 2 Q18
18. The following nine cards are placed in a box.
| A | F | O | N | G | R | O | N | W |
Catherine chooses three cards at random from the box, without replacement.
(a) Calculate the probability that the three cards drawn show the letters ‘A’, ‘F’ and ‘O’ in that order. [2]
(b) Calculate the probability that two of the three cards show the same letter. [3]
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{1}{9} \times \dfrac{1}{8} \times \dfrac{2}{7}\) | M1 | M0 for sight of this method used more than once in the solution. |
| \(= \dfrac{2}{504}\ \left(= \dfrac{1}{252}\right)\) | A1 | ISW if the fractional answer is simplified, otherwise mark final answer. Accept decimal answer of 0·0039(…) OR 0·004 If M0, award SC1 for sight of \(\dfrac{1}{9} \times \dfrac{1}{8} \times \dfrac{2}{7}\) OR \(\dfrac{2}{504}\ \left(= \dfrac{1}{252}\right)\) as part of their solution. |
| Scheme | Marks | Comments | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| ([‘O’ AND ‘O’ AND any other letter] OR [‘N’ AND ‘N’ AND any other letter]) \(3 \times \dfrac{2}{9} \times \dfrac{1}{8}\left(\times \dfrac{7}{7}\right) + 3 \times \dfrac{2}{9} \times \dfrac{1}{8}\left(\times \dfrac{7}{7}\right)\) OR \(3 \times \dfrac{4}{9} \times \dfrac{1}{8}\left(\times \dfrac{7}{7}\right)\) or equivalent | M2 | M1 for \(3 \times \dfrac{2}{9} \times \dfrac{1}{8}\left(\times \dfrac{7}{7}\right)\) OR \(\dfrac{2}{9} \times \dfrac{1}{8}\left(\times \dfrac{7}{7}\right) + \dfrac{2}{9} \times \dfrac{1}{8}\left(\times \dfrac{7}{7}\right)\) OR \(\dfrac{4}{9} \times \dfrac{1}{8}\left(\times \dfrac{7}{7}\right)\) | ||||||||
| \(= \dfrac{12}{72}\ \left(= \dfrac{1}{6}\right)\) | A1 | ISW Accept decimal answer of 0·16(6…) OR 0·17 If no marks, award SC1 for any one of the following answers (from working with replacement):
|
Corrected by Westie's Workshop
- The board's mark scheme printed “Either ‘O’ or ‘N’ chosen”. Changed to “Either ‘O’ or ‘N’ chosen twice” because the value 168/729 is the probability of exactly two O's or exactly two N's, so the label needs the word 'twice' (as in the next row).
Original: see the board's mark scheme PDF (link above).