Intermediate November 2020 Unit 1 Q17
17. Alice works for an engineering company.
A working day is chosen at random.
From keeping a record over the last year, Alice knows that, for this working day,
- the probability that she travels to work by car is 0·7,
- the probability that she arrives at work before 8:00 a.m. is 0·4,
- her time of arrival is independent of how she travels to work.
(a) Using the above information, draw and fully label a complete tree diagram.
You must include all probabilities. [4]
You must include all probabilities. [4]
(b) What is the probability that, on the randomly-chosen working day, Alice travels to work by car and arrives before 8:00 a.m.? [2]
| Scheme | Marks | Comments |
|---|---|---|
Correct framework | B1 | |
| Suitable labelling on both 1st pair of branches AND on both of at least one pair of 2nd set of branches. e.g. ‘Car’, ‘No car’, ‘Before 8’, ‘After 8’. OR Titles of ‘Car’ and ‘Before 8’ with branch endings of ‘Yes’ and ‘No’. | B1 | Accept any unambiguous wording. |
| Correct probabilities on first pair of branches 0·7 AND 0·3 (for ‘Car’, ‘No car’) OR 0·4 AND 0·6 (for ‘Before 8’, ‘After 8’) | B1 | Must be consistent with their labelling. Allow this B1 if no headings given, unless contradicted by, or inconsistent with, further labelling. |
| Correct probabilities on second two sets of branches 0·4 AND 0·6 correctly placed (following 0·7 and 0·3) OR 0·7 AND 0·3 correctly placed (following 0·4 and 0·6) | B1 | Allow this B1 if no headings given, unless contradicted by, or inconsistent with, further labelling. Allow this B1 if only shown on one set of branches. Provided not contradicted on the other set of branches. |
| Scheme | Marks | Comments |
|---|---|---|
| 0·7 × 0·4 or equivalent. | M1 | No FT. |
| = 0·28 or equivalent. | A1 | M1A0 for a final answer of 0·28%. Mark final answer. |