A botanical research station is studying a population of 200 rare plant specimens. The specimens are classified by their height, hhh cm, and their species type (Alpha or Beta), as shown in the table below.
| Height, hhh cm | Species Alpha | Species Beta |
|---|---|---|
| h<15h < 15h<15 | 18 | 32 |
| 15≤h<4015 \le h < 4015≤h<40 | 35 | 45 |
| 40≤h40 \le h40≤h | 27 | 43 |
One specimen is selected at random from the research station.
Find the probability that the specimen is Species Alpha.
Given that the specimen has a height of less than 15 cm, find the probability that it is Species Beta.
Given that the specimen has a height of less than 40 cm, find the probability that it is Species Beta.
State, with a reason, whether or not the event 'Species Beta' is independent of the event 'height is less than 15 cm'.
200 exam-style questions on OCR A Level Maths 2.3 Probability, covering 2.3.1 Mutually exclusive and independent events, 2.3.2 Diagrams to assist probability calculations, 2.3.3 Conditional probability (A-level only), 2.3.4 Conditional probability from first principles (A-level only), and 2.3.5 Modelling with probability. Each one has a worked solution and a mark scheme showing where the marks go.