Mathematical Methods Β· Unit 1 Β· Probability Β· Conditional probability and independence
AI-marked practice questions tied to QCAA mark schemes for this exact LO. Free to start.
Start free practiceFull questions, answers and worked solutions unlock when you start a free practice session.
In a group of 80 students, 45 study Chemistry and 32 study Physics. If 18 students study both subjects, determine the probability that a randomly selected student studies Chemistry or Physics.
In a wildlife survey of 2,400 birds observed in a wetland region, ecologists recorded whether each bird was migratory (event \(M\)) and whether it was observed feeding (event \(F\)). The survey found that 1,680 birds were migratory, 1,560 birds were observed feeding, and 1,200 birds were both migratory and observed feeding. (a) Use the information above to determine \(P(M \cup F)\), the probability that a randomly selected bird from the survey is either migratory or was observed feeding (or both). [2 marks] (b) Hence determine \(P(\overline{M \cup F})\), the probability that a randomly selected bird is neither migratory nor was observed feeding. [1 mark] (c) Use your answer from part (b) to predict the number of birds in the survey that were neither migratory nor observed feeding. [1 mark]
A medical researcher is studying the occurrence of two health conditions, \(X\) and \(Y\), in a population. Information about the probabilities of these conditions is presented in the table below. (a) Use the information in the table to determine \(P(X \cap Y)\). (2 marks) (b) Hence determine the probability that a randomly selected person from the population has at least one of the two conditions. (2 marks)
A veterinary clinic monitors the health conditions of cats brought in for annual check-ups. Historical records show that \(42\%\) of cats have dental disease (event \(D\)), \(28\%\) have a parasite infection (event \(P\)), and \(15\%\) have both conditions. (a) Use the given information to calculate the probability that a randomly selected cat has either dental disease or a parasite infection or both. [2 marks] (b) Determine the probability that a cat has neither dental disease nor a parasite infection. [2 marks] (c) Given that \(35\%\) of cats are overweight (event \(W\)), and that being overweight is independent of having dental disease, calculate the probability that a randomly selected cat has dental disease but is not overweight. [1 mark]