Ecologists are studying the distribution of three plant species EEE, FFF, and GGG within a nature reserve. The probability that a randomly selected quadrat contains species EEE is 0.30.30.3, and the probability it contains species GGG is 0.40.40.4. Observations show that the conditional probability of finding species FFF given that species EEE is present is 0.40.40.4, and the probability that a quadrat contains species EEE or species FFF (or both) is 0.680.680.68.
Species EEE and GGG are known to be mutually exclusive.
Find P(E∪G)\text{P}(E \cup G)P(E∪G).
Show that the probability of a quadrat containing species FFF, P(F)\text{P}(F)P(F), is 0.50.50.5.
Given also that the presence of species FFF and GGG in a quadrat are independent events,
draw a Venn diagram to represent the distribution of these species, indicating the probability associated with each region.
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.