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5 August, 00:54

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?

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  1. 5 August, 04:23
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    (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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