(a) Two taxi companies operate in a certain town. The Grey Taxi Company operates grey vehicles and the Blue Taxi Company operates blue vehicles. 85 per cent of the taxis in the town are grey whereas 15 per cent are blue. A taxi was involved in a hit and run accident on a particular night. A witness identified the taxi as a blue taxi. Tests have reliably shown that 80 per cent of the times, individuals are able to accurately distinguish between grey and blue taxis.
Required: Using Bayes theorem, determine the probability that the taxi that was involved in the accident was actually a blue taxi as per the witness' statement. (4 marks)

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