Higher November 2023 Paper 1 Q10
10. Kate is visiting London.
The probability that she will go on a train is 0·4.
The probability of Kate going to the theatre is independent of her going on a train.
The probability that she goes on a train and goes to the theatre is 0·28.
(a) Complete the following tree diagram. [4]
(b) Calculate the probability that Kate does not go on a train and does not go to the theatre. [2]
| Scheme | Marks | Comments |
|---|---|---|
| 0.6 on the ‘Does not go on a train’ branch | B1 | |
| Use of \(0.4\times\ldots\ldots = 0.28\) OR \(0{\cdot}28\div0{\cdot}4\) | M1 | |
| P(Goes to the theatre) = 0.7 | A1 | Allow M1A1 if 0.7 seen on one of the ‘Goes to the theatre’ branches. |
| 0.7, 0.3, 0.7 and 0.3 correctly placed | A1 | FT ‘their 0.7’ only if M1 awarded. (0.28, 0.72, 0.28, 0.72 is M0A0A0) |
| Scheme | Marks | Comments |
|---|---|---|
| \(0.6\times0.3\) | M1 | FT their tree provided both values between 0 and 1. |
| 0.18 | A1 | |
| (6) |