1MA0 Higher November 2016 Paper 1 Q25
25 Here are 9 cards.
Each card has a shape on it.
In a game the cards are turned over so that the shapes are hidden.
The cards are then mixed up.
Katie turns over at random two of the cards.
Work out the probability that these two cards have different shapes on them.
You must show all your working. (4)
| Answer | Mark | Notes |
|---|---|---|
| \(\dfrac{52}{72}\) | 4 | B1 for \(\dfrac{3}{8}\) or \(\dfrac{2}{8}\) or \(\dfrac{1}{8}\) seen as second probability M1 for \(\dfrac{4}{9} \times \dfrac{3}{8}\) or \(\dfrac{3}{9} \times \dfrac{2}{8}\) or \(\dfrac{2}{9} \times \dfrac{1}{8}\) M1 for \(1 - \left(\dfrac{4}{9} \times \dfrac{3}{8} + \dfrac{3}{9} \times \dfrac{2}{8} + \dfrac{2}{9} \times \dfrac{1}{8}\right)\) or \(\dfrac{4}{9} \times \dfrac{3}{8} + \dfrac{4}{9} \times \dfrac{2}{8} + \dfrac{3}{9} \times \dfrac{4}{8} + \dfrac{3}{9} \times \dfrac{2}{8} + \dfrac{2}{9} \times \dfrac{4}{8} + \dfrac{2}{9} \times \dfrac{3}{8}\) A1 for \(\dfrac{52}{72}\) oe OR B1 for \(\dfrac{5}{8}\) or \(\dfrac{6}{8}\) or \(\dfrac{7}{8}\) seen as second probability M1 for \(\dfrac{4}{9} \times \dfrac{5}{8}\) or \(\dfrac{3}{9} \times \dfrac{6}{8}\) or \(\dfrac{2}{9} \times \dfrac{7}{8}\) M1 for \(\dfrac{4}{9} \times \dfrac{5}{8} + \dfrac{3}{9} \times \dfrac{6}{8} + \dfrac{2}{9} \times \dfrac{7}{8}\) A1 for \(\dfrac{52}{72}\) oe SCB2 \(\dfrac{52}{81}\) oe |