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
is the probability that your Valentine chocolates will
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?