An ecological study analyzed 400 quadrats (sampling areas) in a nature reserve to record the presence of three rare plant species:
The findings are summarized in the following table:
| Species Presence | AAA | BBB | CCC | AAA and BBB | AAA and CCC | BBB and CCC | All three |
|---|---|---|---|---|---|---|---|
| Number of quadrats | 220 | 150 | 130 | 80 | 70 | 60 | 40 |
Represent this information by fully completing a Venn diagram. The region for Alpine Saxifrage only (AAA but not BBB or CCC) has been pre-filled with the number 110.
A quadrat is selected at random from the study. Calculate the probability that the quadrat:
(i) contains Alpine Saxifrage only.
(ii) contains at least two of the three rare plant species.
(iii) contains Alpine Saxifrage or Bluebell or both, given that it does not contain the Common Spotted Orchid.
Determine whether the presence of Bluebells and the presence of Common Spotted Orchids are independent events. Fully justify your answer.
