A botanical research station monitors a collection of 200 rare orchids for three specific fungal infections. Let R R\,R be the event that an orchid has root rot, L L\,L be the event of leaf spot, and S S\,S be the event of stem rust.
The distribution of infections in the collection is as follows:
One orchid is selected at random from the collection.
Determine the probability that the orchid does not have stem rust.
Find P(R∩L∩S′)P(R \cap L \cap S')P(R∩L∩S′).
Find P(R∪L∪S′)P(R \cup L \cup S')P(R∪L∪S′).
Calculate the probability that the orchid has at most one type of infection.
Given that the selected orchid has at most one type of infection, find the probability it has root rot.
The random variable X X\,X represents the number of different types of infections found on a randomly selected orchid.
Find the expected value E(X)E(X)E(X).
Practise Edexcel A Level Maths Conditional Probability with exam-style questions for A Level Maths. 100 questions covering Set Notation, Conditional Probability, Conditional Probabilities in Venn Diagrams, Probability Formulae, and Tree Diagrams, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.