Higher June 2017 Paper 4 Q13
13 Rashid drives his car along a road passing through two sets of traffic lights.
The tree diagram shows the probabilities of the lights being red when he reaches them.
(a) Complete the tree diagram. [1]
(b) Write down the probability that the first set is not red. [1]
(c) Given that the first set is red, write down the probability that the second set is not red. [1]
(d) Work out the probability that both sets are not red. [2]
(e) Work out the probability that at least one set is not red. [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [0].4, [0].3 and [0].8 oe in the correct places | 1 | Accept equivalent fractions or percentages with % sign in each part and FT their tree diagram only if (a) scores 0 marks | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [0].4 or \(\frac{2}{5}\) oe | 1 | FT their tree diagram | accept 40%: condone \(\frac{.4}{1}\), penalise wrong form once eg 4 : 10, 4 in 10 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [0].7 or \(\frac{7}{10}\) oe | 1 | accept 70% | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [0].08 or \(\frac{2}{25}\) oe | 2 | FT their tree diagram for 2 marks M1 for their[0].4 × [0].2 | accept 8% and working may be in the tree |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [0].82 or \(\frac{41}{50}\) oe | 3 | FT their tree diagram for 3 marks | accept any correct method and working may be in tree |
| M2 for 1 – [0].6 × their [0].3 or [0].6 × [0].7 + their [0].4 × their [0].8 + their [0].4 × [0].2 oe soi | implied by 1 - [0].18 implied by [0].42 + [0].32 + [0].08 | ||
| or | |||
| M1 for [0].6 × their [0].3 or two of [0].6 × [0].7, their [0].4 × their [0].8, their [0].4 × [0].2 oe soi | implied by [0].18 implied by two of [0].42, [0].32, [0].08 | ||