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'.
368 exam-style questions on Edexcel A Level Maths Conditional Probability, covering 2.1 Set Notation, 2.2 Conditional Probability, 2.3 Conditional Probabilities in Venn Diagrams, 2.4 Probability Formulae, and 2.5 Tree Diagrams. Each one has a worked solution and a mark scheme showing where the marks go.