dent? Justify your answer. 17. A survey of automobile ownership was conducted fo
ID: 3277414 • Letter: D
Question
dent? Justify your answer. 17. A survey of automobile ownership was conducted for 200 families in Houston. The nal results of the study showing ownership of automobiles of United States and foreign manufacture are summarized as follows: Do you own a foreign car? Yes 30 104 |150 101160 Totals 180 20200 a. Show the joint probability table for the above data. b. Use the marginal probabilities to compare U.S. and foreign car ownership c. What is the probability that a family will own both a U.S. car and a foreign car? d. What is the probability that a family owns a car, U.S. or foreign? e. If a family owns a U.S. car, what is the probability that it also owns a foreign car? f. If a family owns a foreign car, what is the probability that it also owns a U.S. car? Are U.S. and foreign car ownership independent events? Explain.Explanation / Answer
a) dividing each cell value by 200 ; below is the joint pdf:
b)
marginal probability for foreign car from above:
therefore from above probability of having a US car 0.9 whille of having a foreign car is 0.2.
c) from above joint pdf table probability =0.15
d)probability =1-P( not owning a car )=1-0.05=0.95
e)probability =P( foreign car|US car) =0.15/0.9=1/6
f)probability =P( US car|foreign car)=0.15/0.20=3/4
g)No as P( foregin car)*P( US car) =0.9*0.2=0.18 is not equal to P(US car and Foreign car) which is equal to 0.15.
therefore not independent.
US car yes No total foreign car Yes 0.15 0.05 0.2 No 0.75 0.05 0.8 total 0.9 0.1 1Related Questions
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