Exam 1 solutions

exam 1 solutions
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1. Your special Valentine is late mailing you a box of chocolates. You estimate that there is a 75% chance that SX shipping will be chosen and a 25% chance that UVS shipping will be chosen (because it is more expensive). From your experience with them, SX has about a 24% chance of getting the box to you on time if it is chosen; while UVS, which is faster, has about a 45% chance of getting you the box on time if it is chosen. a) (10 pts.) What is the probability the candy will arrive on time in an SX package? P(Timely,SX) = P(SX)P(Timely|SX) = .75x.24 = .18 What is the probability the candy will arrive on time in a UVS parcel? P(Timely,UVS) = P(UVS)P(Timely|UVS) = .25x.45 = .1125 Therefore, what is the probability that your Valentine chocolates will not arrive on time? P(Timely) = P(Timely,SX) + P(Timely,UVS) = .18 + .1125 = .2925 P(Late) = 1 – P(Timely) = .7075 b) (10pts) Valentines day comes to an end, and no candy has arrived. What is the probability that this is because your sweetheart chose SX shipping?
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