Jimmy and his rock band are driving up the Bruce Highway in a van to play a gig

Question

Jimmy and his rock band are driving up the Bruce Highway in a van to play a gig in Cairns. During the journey, the copious amount of apple juice Jimmy has consumed catches up with him, and he announces that he must go to the toilet as soon as possible. The driver of the van says "we can't pull over until a service station". The Bruce Highway has a variety of service stations, BP (35%), Shell (30%), Mobile (20%) and the rest are independent service stations. Past experience has indicated that not all service stations have an operating toilet. BP has very high standards, with 95% of BP having toilets in operation. For Shell and Mobile, these numbers are slightly less at 88% and 80%, respectively. Independent service stations only have a 60% chance of an operating toilet. Answer the following, stating all probability rules that you use. (a) What's the probability that the next service station will not have an operating toilet? (b) If the next station does have an operating toilet, what is the chance it is either an independent or Mobile service station?

Explanation / Answer

a) probabilty that next service station will not hav operating toilet

=0.35*(1-0.95)+0.3*(1-0.88)+0.2*(1-0.8)+0.15*(1-0.60)=0.1535

b) hence probabilty that it is either an independent or mobile service station =(0.2*(1-0.8)+0.15*(1-0.60))/0.1535

=0.6515

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