4400 Higher November 2008 Paper 4 Q11
11 A coin is biased.
When it is thrown, the probability that it shows Heads is \(\dfrac{2}{3}\)
Dorcas throws the coin twice.
(a) Complete the probability tree diagram.
(b) Find the probability that the coin shows Heads both times. (2)
(c) Find the probability that the coin shows Heads at least once. (3)
| Scheme | Marks |
|---|---|
| P(T) = \(\frac{1}{3}\) | B1 |
| correct structure | B1 |
| all probs & labels correct | B1 |
| (3) |
| Scheme | Marks |
|---|---|
| \(\frac{2}{3} \times \frac{2}{3}\) | M1 |
| \(\frac{4}{9}\) oe | A1 |
| (2) |
Notes
A1: 0.44
| Scheme | Marks |
|---|---|
| \(\left(\frac{2}{3}\right)^2\) or (b) or \(\frac{2}{3} \times \frac{1}{3}\) | M1 |
| \(\frac{2}{3} \times \frac{1}{3} \times 2 + \left(\frac{2}{3}\right)^2\) or + (b) | M1 |
| \(\frac{8}{9}\) oe | A1 |
| (3) | |
| (8 marks) |
Notes
M1: \(1 - \left(\frac{1}{3}\right)^2\) M2
A1: 0.89, allow 0.88