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3. A certain auto mall sells only Fords, Hondas, and Toyotas. Each customer buys only 1 car It is known that 45% of all customers buy a Toyota and 35% buy a Ford. It is also known that 40% of the Toyota customers buy a white car whereas only 30% of the Honda customers buy a white car. None of the Ford customers buy a white car a. Express all numbers given in the problem statement as probabilities of events. (2 pts) b. What is the probability that the customer bought a white car? (2 pts) c. If the customer bought a white car, what is the probability that he or she bought a Toyota? (2 pts) It is observed that 65% of all customers buy an automatic shift car. However, 80% of white Tovota buvers purchase an automatic shift d. What is the probability that the customer buys a white Toyota with an automatic shift? (2 pts) What is the probability that the customer bought a white Toyota given that he or she bought an automatic shift car? (2 pts) e. Draw Venn diagrams and express in set notation the events that f. A customer buys a white Toyota with manual (non-automatic) transmission. (2 pts) g. A customer buys either a non-white Honda or a Ford with automatic transmission. (2 pts)

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a let F, H,T denote the events that the austomer buys let w be the event that tre customes buys foad a Homdaa o toyota coor respectively PCT.5 PCW)H)03 b PCH)03s 0.2 By law of total pobabilty, C) By Bayes thersem, o 24 0-75 (d) let A be the event that the customer buys autorratic shift ca PAIT and w) P obabitity thot the customes buys chite toyo ta asith an autaintfc shist- PCT and W and A)

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