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 (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.