A botanical researcher is studying a large population of orchids. In this population, 15%15\%15% of the orchids exhibit the rare "Purple" phenotype (PPP) and the remaining 85%85\%85% exhibit the standard "White" phenotype (WWW). The researcher selects two orchids at random from this population for genetic testing.
Calculate the probability that both selected orchids exhibit the same phenotype.
Determine the probability that both orchids are Purple, given that at least one of the orchids is found to be Purple.
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.