A local GP is concerned that the other doctors in the general practice where she works provide a proportionally higher number of short consultations. A random sample of 200 consultations is extracted from the records and the results are detailed in the following contingency table. Calculate the conditional probability that a short consultation is provided given that the patient sees Dr Howell. Repeat the calculations for each other doctor. Overall, what is the probability that a consultation is short? Does there appear to be a relationship between the doctor a person sees and whether the consultation is short or long? Write a short interpretation of your findings for the local GP.

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Consultation Total Doctor Long Short 71 55 74 200 Dr Howell Dr Tran Dr Jackson Total patients 38 22 33 33 36 102 38 98