The three most popular options on a certain type of new car are a built in GPS A a sunroof B and an automatic transmission C If 46 of all purchasers request A 58 request B 74 reque C 65 request A or B 80 request A or C 87 request B or C and 89 request A or B or C determine the probabilities of the following events Hint A or B is the event that at least one of th two options is requested try drawing a Venn diagram and labeling all regions a The next purchaser will request at least one of the three options 0 89 b The next purchaser will select none of the three options 0 11 c The next purchaser will request only an automatic transmission and not either of the other two options 0 05 x d The next purchaser will select exactly one of these three options