4MA0 Higher January 2015 Paper 4R Q13
13 Jim has a biased coin.
The probability that Jim will throw Heads on any throw is \(p\).
Jim throws the coin twice.
(a) Complete the probability tree diagram.
Give your probabilities in terms of \(p\).
Give your probabilities in terms of \(p\).
(b) Find an expression, in terms of \(p\), for the probability that Jim will throw two Heads. (1)
Given that \(p = 0.8\),
(c) work out the probability that Jim will throw exactly one Head. (3)
| Scheme | Marks |
|---|---|
| \(p\) and \(1 - p\) on the branches | B1 |
| B1 | |
| (2) |
Notes
B1: \(1 - p\) on LH branch
B1: for \(p\) and \(1 - p\) in correct places on RH branches
| Scheme | Marks |
|---|---|
| \(p^2\) | B1 |
| (1) |
Notes
B1: accept \(p \times p\)
| Scheme | Marks |
|---|---|
| \(p \times (1 - p)\) oe or \(p \times \text{“}(1 - p)\text{”}\) or 0.2 × 0.8 (=0.16) | M1 |
| \(p \times (1 - p) + (1 - p) \times p\) or \(p \times \text{“}(1 - p)\text{”} + \text{“}(1 - p)\text{”} \times p\) or 0.8 × 0.2 + 0.2 × 0.8 or 2 × “0.16” | M1 |
| 0.32 oe | A1 |
| (3) | |
| (6 marks) |
Notes
M1: ft from tree diagram
M1: ft from tree diagram
A1: cao