1MA0 Higher June 2013 Paper 1 Q26
26 Fiza has 10 coins in a bag.
There are three £1 coins and seven 50 pence coins.
Fiza takes at random, 3 coins from the bag.
Work out the probability that she takes exactly £2.50 (4)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| 50 1 1 1 50 1 1 1 50 | \(\dfrac{126}{720}\) | 4 | M1 for 3 fractions \(\dfrac{a}{10}, \dfrac{b}{9}, \dfrac{c}{8}\) where \(a \lt 10\), \(b \lt 9\) and \(c \lt 8\) M1 for \(\dfrac{7}{10} \times \dfrac{3}{9} \times \dfrac{2}{8}\) or \(\dfrac{3}{10} \times \dfrac{7}{9} \times \dfrac{2}{8}\) or \(\dfrac{3}{10} \times \dfrac{2}{9} \times \dfrac{7}{8}\) \(\left(= \dfrac{42}{720}\right)\) M1 for \(\dfrac{7}{10} \times \dfrac{3}{9} \times \dfrac{2}{8} + \dfrac{3}{10} \times \dfrac{7}{9} \times \dfrac{2}{8} + \dfrac{3}{10} \times \dfrac{2}{9} \times \dfrac{7}{8}\) or \(3 \times \dfrac{3}{10} \times \dfrac{2}{9} \times \dfrac{7}{8}\) A1 for \(\dfrac{126}{720}\) oe. eg. \(\dfrac{7}{40}\) Alternative Scheme for With Replacement M1 for \(\dfrac{7}{10} \times \dfrac{3}{10} \times \dfrac{3}{10}\) \(\left(= \dfrac{63}{1000}\right)\) M1 for \(\dfrac{7}{10} \times \dfrac{3}{10} \times \dfrac{3}{10} \times 3\) \(\left(= \dfrac{189}{1000}\right)\) M0 A0 No further marks |