A boutique coffee house tracks the monthly habits of its 120 loyalty card holders. The frequency of their visits and their preferred beverage type are summarized in the table below.
| Monthly visits, vvv | Espresso-based | Filter coffee |
|---|---|---|
| v<10v < 10v<10 | 18 | 32 |
| 10≤v<2010 \le v < 2010≤v<20 | 22 | 18 |
| v≥20v \ge 20v≥20 | 14 | 16 |
One of the 120 members is selected at random.
Find the probability that the member prefers Filter coffee.
Given that the member visits fewer than 10 times a month, find the probability that this member prefers Espresso-based drinks.
Given that the member visits fewer than 20 times a month, find the probability that this member prefers Espresso-based drinks.
State, with a reason, whether or not the event 'prefers Espresso-based drinks' is independent of the event 'visits fewer than 10 times a month'.
200 exam-style questions on OCR (MEI) A Level Maths 2.3 Probability, covering 2.3.1 Calculate the probability of an event, 2.3.2 Complementary events, 2.3.3 Expected frequency of an event, 2.3.4 Diagrams to calculate probabilities, 2.3.5 Mutually exclusive and independent events, 2.3.6 Add probabilities for mutually exclusive events, 2.3.7 Multiply probabilities for independent events, 2.3.8 Mutually exclusive and independent events (notation) (A-level only), 2.3.9 Venn diagrams for probabilities (A-level only), 2.3.10 Conditional probabilities (A-level only), and 2.3.11 Independence via conditional probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.