1MA0 Higher June 2014 Paper 1 Q23
23 Yvonne has 10 tulip bulbs in a bag.
7 of the tulip bulbs will grow into red tulips.
3 of the tulip bulbs will grow into yellow tulips.
Yvonne takes at random two tulip bulbs from the bag.
She plants the bulbs.
(a) Complete the probability tree diagram.
(b) Work out the probability that at least one of the bulbs will grow into a yellow tulip. (3)
| Answer | Mark | Notes |
|---|---|---|
| \(\dfrac{3}{10}\), \(\dfrac{6}{9}\), \(\dfrac{3}{9}\), \(\dfrac{7}{9}\), \(\dfrac{2}{9}\) | 2 | B1 for \(\dfrac{3}{10}\) on LH yellow branch B1 for \(\dfrac{6}{9}\), \(\dfrac{3}{9}\), \(\dfrac{7}{9}\), \(\dfrac{2}{9}\) correct on tree diagram |
| Answer | Mark | Notes |
|---|---|---|
| \(\dfrac{48}{90}\) | 3 | M1 for \(\dfrac{7}{10} \times \text{``}\dfrac{3}{9}\text{''}\) or \(\text{``}\dfrac{3}{10}\text{''} \times \text{``}\dfrac{7}{9}\text{''}\) or \(\text{``}\dfrac{3}{10}\text{''} \times \text{``}\dfrac{2}{9}\text{''}\) M1 for \(\dfrac{7}{10} \times \text{``}\dfrac{3}{9}\text{''} + \text{``}\dfrac{3}{10}\text{''} \times \text{``}\dfrac{7}{9}\text{''} + \text{``}\dfrac{3}{10}\text{''} \times \text{``}\dfrac{2}{9}\text{''}\) A1 for \(\dfrac{48}{90}\) oe OR M1 for \(\dfrac{7}{10} \times \text{``}\dfrac{6}{9}\text{''}\) M1 for \(1 - \dfrac{7}{10} \times \text{``}\dfrac{6}{9}\text{''}\) A1 for \(\dfrac{48}{90}\) oe |