For customers purchasing a refrigerator at a certain appliance store, let A be the event that the refrigerator was manufactured in the U.S., B be the event that the refrigerator has an icebreaker, and the event that the customer purchased an extended warranty. Relevant probabilities are:
P(A)= 0.75
P(B|A) = 0.9
P(B|A′) = 0.8
P(C|A ∩ B) = 0.8
P(C|A ∩ B′) = 0.6
P(C|A′ ∩ B) = 0.7
P(C|A′ ∩ B′) = 0.3
What is the probability that the refrigerator was manufactured in the US, with an icebreaker, and the customer purchased an extended warranty?
What is the probability that the refrigerator does not have an icebreaker, or the customer did not purchase an extended warranty?
What is the probability that the customer purchased an extended warranty?
What is the probability that the refrigerator does not have an icebreaker given that it was not
manufactured in the US?
1) probability that the refrigerator was manufactured in the US, with an icebreaker, and the customer purchased an extended warranty =P(A n B n C) =P(A)*P(B|A)*P(C|An B) =0.75*0.9*0.8 =0.54
2)
probability that the refrigerator does not have an icebreaker, or the customer did not purchase an extended warranty
P(Bc u Cc) =1-P(B n C) =1-(P(A n B n C)+P(A' n B n C))=1-(0.75*0.9*0.8+0.25*0.8*0.7)=0.32
3)
probability that the customer purchased an extended warranty =P(C)
=0.75*0.9*0.8+0.75*0.1*0.6+0.25*0.8*0.7+0.25*0.2*0.3 =0.74
4)
probability that the refrigerator does not have an icebreaker given that it was notmanufactured in the US
=P(Bc|Ac) =P(Ac n Bc)/P(Ac) =0.25*0.2/0.25 =0.2
For customers purchasing a refrigerator at a certain appliance store, let A be the event that...
For customers purchasing a refrigerator at a certain appliance store, et A be the event that the refrigerator was manufactured in the U that the customer purchased an extended warranty. Relevant probabilities are below. be the event that the refrigerator had an ice maker, and C be the event P(A) 0.71 PB | A)-0.90 P(B I A)-0.82 P(C IA'n B)-0.69 PCIA'nB)-0.31 (a) Construct a tree diagram consisting of first-, second, and third-generation branches and place an event label and appropriate...
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Probability in the Appliance Store Problems 1-13: An appliance store recorded data for their customers who purchased warranties and had complaints about their appliances. The following data classifies the categories of complaints with whether the complaint occurred during or after the warranty. There were 100 complaints. Express your answers as decimals. If necessary, round to four decimal positions. Problems 14 and 15 are short answer, requiring justification. Electrical Mechanical Appearance During Warranty 18 13 31 After Warranty 12 22 ...
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