Question

(a) Suppose that out of all students, 40% have a bicycle, 25% have a motorbike and 10% have both. Let A be the event that a randomly-chosen student has a bicycle and let B be the event that he/she has a motorbike

(i) Find the proportion of bicycle owners who have a motorbike.Write [2] this as a conditional probability and interpret it.

(ii) Find the proportion of motorbike owners who have a bicycle. Write [2] this as a conditional probability and interpret it.

(iii) Are the events A and B mutually exclusive? Justify your answer in [2] at most one sentence.

(iv) Are the events A and B independent? Justify your answer in at most [2] one sentence.

(b) Current medical research on the coronavirus COVID-19 indicates that [10]

• if a person has COVID-19 then the probability of observing the symp- tom of high temperature is 0.35, • if a person does not have COVID-19 then the probability of observing the symptom of high temperature is 0.05, and

• currently 0.5% of people have COVID-19. A doctor is presented with a patient showing the symptom of high temper- ature. What is the probability that this particular patient has COVID-19? Indicate clearly all of the steps of your work.

Answer 1

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