Suppose that 1/2 of all cars sold at a nissan dealer in a given year are altimas, 1/3 are maximas, and the rest are sentras. suppose that 3/4 of the altimas, 1/2 of the maximas, and 1/2 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?

(1) Not conditional, 5/8

(2) Not conditional, 1/12

(3) Conditional, 1/18

Step-by-step explanation:

Fraction of cars sold

Altima = 1/2

Maxima = 1/3

Sentra = 1 - (1/2 + 1/3) = 1 - 5/6 = (6 - 5)/6 = 1/6

Fraction of cars sold with moon roof

Altima = 3/4 × 1/2 = 3/8

Maxima = 1/2 × 1/3 = 1/6

Sentra = 1/2 × 1/6 = 1/12

(1) Probability (a randomly selected car has a moon roof) = 3/8 + 1/6 + 1/12 = (9+4+2)/24 = 15/24 = 5/8

(2) Probability (a randomly selected car has a moon roof given it is Sentra) = 1/12

(3) Probability (a randomly selected car is a Maxima if it has a moon roof) = 1/3 × 1/6 = 1/18

A conditional probability uses if (as a condition) in making statements or asking questions

An unconditional probability makes statement or ask question without the use of condition (if)

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