A sample of 400 cars is classified by fuel type and by whether the engine capacity is above 1.6 litres. The table below is incomplete.
| Engine capacity above 1.6 litres | Engine capacity at most 1.6 litres | Total | |
|---|---|---|---|
| Diesel | 160 | ||
| Petrol | 180 | ||
| Total | 120 | 400 |
One of these 400 cars is selected at random. The event D D\,D is that the car is diesel, and the event E E\,E is that its engine capacity is above 1.6 litres.
Complete the table.
Find P(D∩E′)P(D \cap E')P(D∩E′).
Find P[(D∪E)′]P\left[(D \cup E)'\right]P[(D∪E)′].
Determine whether D D\,D and E E\,E are independent.
198 exam-style questions on AQA A Level Maths 2.3 M: Probability, covering 2.3.1 Mutually exclusive and independent events, 2.3.2 Conditional probability (A-level only), 2.3.3 Modelling with probability (A-level only), and 2.3 M: Probability. Each one has a worked solution and a mark scheme showing where the marks go.