Higher June 2019 Paper 1 Q10
10. Sam needs to catch the 8 a.m. bus to get to work on time.
The probability that Sam oversleeps is 0·6.
When Sam oversleeps, the probability that he misses the bus is 0·8.
When Sam does not oversleep, the probability that he misses the bus is 0·3.
(a) Complete the following tree diagram to show this information. [2]
(b) Calculate the probability that Sam oversleeps and misses the bus. [2]
(c) Calculate the probability that Sam catches the bus.
You must show all your working. [3]
You must show all your working. [3]
| Scheme | Marks | Comments |
|---|---|---|
Correctly completes the tree diagram | B2 | B1 for any two pairs of branches correct |
| Scheme | Marks | Comments |
|---|---|---|
| \(0.6\times0.8\) | M1 | FT ‘their 0.8’ from their tree diagram provided it is greater than 0 and less than 1 |
| 0.48 oe | A1 | FT |
| Scheme | Marks | Comments |
|---|---|---|
| \((0.6\times0.2) + (0.4\times0.7)\) | M2 | M1 for either \((0.6\times0.2)\) or \((0.4\times0.7)\) seen For M1 or M2, FT ‘their probabilities from their tree’ provided they are greater than 0 and less than 1 |
| 0.4 oe | A1 | FT |
| (7) |