Higher June 2017 Paper 1 Q17
17 There are 9 counters in a bag.
7 of the counters are green.
2 of the counters are blue.
Ria takes at random two counters from the bag.
Work out the probability that Ria takes one counter of each colour.
You must show your working. (4)
| Answer | Mark | Notes | |
|---|---|---|---|
| \(\dfrac{28}{72}\) | P1 | for \(\dfrac{6}{8}\) or \(\dfrac{2}{8}\) or \(\dfrac{7}{8}\) or \(\dfrac{1}{8}\) oe seen on diagram or in a calculation | |
| P1 | for \(\dfrac{7}{9} \times \dfrac{2}{8}\) or \(\dfrac{2}{9} \times \dfrac{7}{8}\) or \(\dfrac{14}{72}\) oe | for \(\dfrac{7}{9} \times \dfrac{6}{8}\) or \(\dfrac{2}{9} \times \dfrac{1}{8}\) or \(\dfrac{42}{72}\) or \(\dfrac{2}{72}\) or \(\dfrac{44}{72}\) oe | |
| P1 | for \(\dfrac{7}{9} \times \dfrac{2}{8} + \dfrac{2}{9} \times \dfrac{7}{8}\) or \(\text{``}\tfrac{14}{72}\text{''} + \text{``}\tfrac{14}{72}\text{''}\) oe | for \(1 - \left(\dfrac{7}{9} \times \dfrac{6}{8} + \dfrac{2}{9} \times \dfrac{1}{8}\right)\) or \(1 - \left(\text{``}\tfrac{42}{72}\text{''} + \text{``}\tfrac{2}{72}\text{''}\right)\) or \(1 - \text{``}\tfrac{44}{72}\text{''}\) oe | |
| A1 | oe SC B1 for \(\dfrac{14}{81}\) B2 for \(\dfrac{28}{81}\) | ||