Higher November 2022 Unit 2 Q8
8. Bag A and Bag B contain only red and blue balls.
The probability of choosing a red ball from Bag A is \(\dfrac{3}{5}\).
The probability of choosing a red ball from Bag B is 0·25.
A ball is chosen at random from each bag.
(a) Complete the tree diagram below. [2]
(b) Find the probability that the two balls chosen are the same colour. [3]
| Scheme | Marks | Comments |
|---|---|---|
Complete diagram | B2 | Award B1 for one of the following:
|
| Scheme | Marks | Comments |
|---|---|---|
| Sight of \(\dfrac{3}{5} \times 0{\cdot}25\) OR \(\dfrac{2}{5} \times 0{\cdot}75\) or equivalent | B1 | Check diagram for answers. FT ‘their 2/5’ from bag A blue branch, only if between 0 and 1. FT ‘their 0.75’ from bag B blue branch, only if between 0 and 1. Award B1 for sight of 0·15 OR 0·3 or equivalent. |
| \(\dfrac{3}{5} \times 0{\cdot}25\ \ \mathbf{+}\ \ \dfrac{2}{5} \times 0{\cdot}75\) or equivalent | M1 | Award M1 for 0·15 + 0·3. |
| 0·45 or 9/20 or equivalent ISW | A1 | Only FT, provided answer is less than 1. |