A fitness center has 100 members. The length of time they have been members and their preferred exercise type are summarized in the table below.
| Membership duration, xxx years | Yoga | Cardio |
|---|---|---|
| x<2x < 2x<2 | 8 | 12 |
| 2≤x<52 \le x < 52≤x<5 | 15 | 25 |
| 5≤x5 \le x5≤x | 12 | 28 |
One of the 100 members is selected at random.
Find the probability that the member prefers Yoga.
Given that the member has been a member for less than 2 years, find the probability that this member prefers Cardio.
Given that the member has been a member for less than 5 years, find the probability that this member prefers Cardio.
State, with a reason, whether or not the event 'preferring Cardio' is independent of the event 'being a member for less than 2 years'.
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.