A garage sells three types of fuel; U95, U98 and diesel. In a survey of 200 motorists buying fuel at the garage, 80 are female and the rest are male. Of the 90 motorists buying 'U95' fuel, 50 were female and of the 70 motorists buying diesel, 60 were male. A motorist does not buy more than one type of fuel. Find the probability that a randomly chosen motorist a buys U98 fuel, b is male, given that the motorist buys U98 fuel. Garage records indicate that 10% of the motorists buying U95 fuel, 30% of the motorists buying U98 fuel and 40% of the motorists buying diesel have their car serviced by the garage. A motorist is chosen at random. c Find the probability that this motorist has his or her car serviced by the garage. d Given the motorist has his or her car serviced by the garage, find the probability that the motorist buys diesel fuel.

AppendixLO1