Suppose that 1212 of all cars sold at a Nissan dealer in a given year

Monincbh

Monincbh

Answered question

2021-11-17

Suppose that 1212 of all cars sold at a Nissan dealer in a given year are Altimas, 1313 are Maximas, and the rest are Sentras. Suppose that 1212 of the Altimas, 1212 of the Maximas, and 2323 of the Sentras have a moon roof. Answer the following questions. For each question, first decide whether the probability is a conditional probability or not.
1. What is the probability a randomly selected car has a moon roof?
2. What is the probability that a randomly selected car has a moon roof given it is a Sentra?
3. What is the probability a randomly selected car is a Maxima if it has a moon roof?

Answer & Explanation

Salvador Fry

Salvador Fry

Beginner2021-11-18Added 12 answers

Step 1
Let A denote the car sold is Altimas
B denote that the car sold is Maximas
C denote that the car sold is Sentras
And X denote that the car has a moon roof.
The following information is provided in the question
P(A)=12,P(XA)=12
P(B)=13,P(XB)=12
P(C)=16,P(XC)=23
(1) Using the Law of Total Probability, the probability that a randomly selected car has a moon roof is given as
P(X)=P(A)×P(XA)+P(B)×P(XB)+P(C)×P(XC)
=12×12+13×12+16×23
=1936
Step 2
(2) The probability that a randomly selected car has a moon roof given it is a Sentra is given as
P(XC)=23
Step 3
(3) The probability a randomly selected car is a Maxima if it has a moon roof is given by
P(BX)=P(B)×P(XB)P(X)
=13×121936
=619

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