Higher June 2024 Paper 1 Q19
19. Anya and Elis sit examinations at a college.
(a) Anya sits two examinations, one for Spanish and the other for French.
The probability that Anya passes Spanish is 0·6.
The probability that Anya passes French is 0·7.
The probability of Anya passing Spanish is independent of her passing French.
Anya tries to calculate the probability of her passing exactly one examination.
She writes \(0{\cdot}6\times0{\cdot}3 = 0{\cdot}18\)
The probability that Anya passes Spanish is 0·6.
The probability that Anya passes French is 0·7.
The probability of Anya passing Spanish is independent of her passing French.
Anya tries to calculate the probability of her passing exactly one examination.
She writes \(0{\cdot}6\times0{\cdot}3 = 0{\cdot}18\)
(i) Without giving any calculations, explain why this answer is not fully correct. [1]
(ii) Calculate the probability of Anya passing exactly one examination. [2]
(b) Elis sits one examination.
The examination has 75 multiple choice questions.
For each question:
The examination has 75 multiple choice questions.
For each question:
- there are five possible answers to choose from
- only one of the five possible answers is correct.
Elis knows the answer to 60% of the questions and will get these correct.
Of the remaining questions, he randomly selects one of the five possible answers.
A question is selected at random.
What is the probability that Elis answers this question correctly? [4]
| Scheme | Marks | Comments |
|---|---|---|
| (a)(i) Anya is incorrect with idea that they could be in any order i.e. SF’ + S’F e.g. ‘Anya has calculated the probability of passing Spanish only’ ‘Anya hasn’t calculated the probability of passing French only’ | E1 | Do not allow the E1 for numerical ‘explanations’ only i.e. ‘It should be 0.6 × 0.3 + 0.4 × 0.7’ Do not accept ‘she hasn’t added the results together’ unless explanation given for what is meant by ‘results’ |
| (a)(ii) (0.6 x 0.3) + (0.4 x 0.7) | M1 | Award marks if seen in a(i) and not replaced. |
| 0.46 oe | A1 | CAO |
| Scheme | Marks | Comments |
|---|---|---|
| \(0{\cdot}6\times75 + 0{\cdot}2\times(75 - 0{\cdot}6\times75)\) \((= 45 + 6)\) | M3 | Allow for appropriate sight of 45 AND/OR 6 throughout M2 for \(0{\cdot}6\times75\) AND \(0{\cdot}2\times(75 - 0{\cdot}6\times75)\) (=45) (=6) M1 for one of the following:
|
| \(\dfrac{51}{75}\) oe ISW | A1 | CAO |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| \(0{\cdot}6 + (1 - 0{\cdot}6)\times0.2\). oe | M3 | M2 for \((1 - 0{\cdot}6)\times0{\cdot}2\) oe. \((= 0{\cdot}08)\) M1 for \(0.6 + 0.2\times\ldots\) or \(0.6 + (1 - 0.6)\times\ldots\) oe |
| \(0{\cdot}68\) | A1 |
| (7) |