Foundation November 2023 Paper 1 Q30
30. 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 \(0{\cdot}4 \times \ldots\ldots = 0{\cdot}28\) OR \(0{\cdot}28 \div 0{\cdot}4\) | 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 |
|---|---|---|
| \(0{\cdot}6 \times 0{\cdot}3\) | M1 | FT their tree provided both values between 0 and 1. |
| 0.18 | A1 | |
| (6) |