4400 Higher June 2004 Paper 4 Q14
14 Here is a fair 3-sided spinner.
Its sides are labelled 1, 2 and 3 as shown.
(a) Aisha is going to spin the spinner twice.
Work out the probability that it will land on 1 both times. (2)
Work out the probability that it will land on 1 both times. (2)
(b) Harry is going to spin the spinner 3 times.
(i) Complete the probability tree diagram.
(ii) Work out the probability that the spinner will land on an odd number 3 times.
(iii) Work out the probability that the spinner will land on an even number exactly once. (9)
| Scheme | Marks |
|---|---|
| \(\frac{1}{3} \times \frac{1}{3}\) or all 9 combinations shown eg 2 way table or list | M1 |
| \(\frac{1}{9}\) | A1 |
| (2) |
| Scheme | Marks |
|---|---|
| (i) \(\frac{2}{3}\) on bottom LH branch | B1 |
| rest of probabilities correct | B1 |
| EOE, EOO, OEE, OEO, OOE, OOO | B1 |
| (ii) \(\frac{2}{3} \times \frac{2}{3} \times \frac{2}{3}\) | M1 |
| \(\frac{8}{27}\) oe | A1 |
| (iii) \(\frac{1}{3} \times \frac{2}{3} \times \frac{2}{3}\) in any order or \(\frac{4}{27}\) | M1 |
| 3 correct paths identified | B1 |
| "\(\frac{4}{27}\)" × 3 | M1 |
| \(\frac{4}{9}\) oe | A1 |
| (9) | |
| (11 marks) |
Notes
A1: ft if 0 < probs < 1
B1: may be implied by next M1
M1: or add 3 correct paths
A1: ft if 0 < probs < 1