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Math Help - [SOLVED] Probability Venn Diagrams Please Double Check

  1. #1
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    [SOLVED] Probability Venn Diagrams Please Double Check

    1.A survey of local car dealers revealed that 64% of all cars sold last month had CD players, 28% had alarm systems, and 22% had both CD players and alarm systems. Answer the questions below


    b)What is the probability one of these cars selected at random had neither a CD player nor an alarm system? [1 point]
    My answer: 1-(.42 +.22 +.06) = .70


    c)What is the probability that a car had a CD player unprotected by an alarm system? [1]
    My answer: .64 - .22 = .42




    d)What is the probability a car with an alarm system had a CD player? [1 point]
    My answer: .22





    e)Are having a CD player and an alarm system disjoint events? Are they independent? Explain. [2 points]


    My thoughts:

    They aren't independent because

    P(both) doesn't equal P(Alarm) * P(Cd)
    .22 doesnt equal .0252



    They are disjoint because they are not independent and P(Alarm and Cd) does not equal 0
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  2. #2
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    Here is the setup: P(CD)=0.64~,~P(AS)=0.28\text{  and  }P(CD~\&~AS)=0.22.
    So P(CD\text{ or }AS)=P(CD)+P(AS)-P(CD~\&~AS)=0.70.
    That is the probability of a car having at least one of the systems.
    So 1-0.70=0.30 is the probability of a can having neither.
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  3. #3
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    Hello, rice4lifelegit!

    A survey revealed that 64% of all cars sold last month had CD players (CD),
    28% had alarm systems (AS), and 22% had both CD and AS.
    Answer the questions below.
    I assume that part (a) was to draw the Venn diagram.
    Code:
          * - - - - - - - - - - - - - - - *
          |                               |
          |   * - - - - - - - *           |
          |   | CD            |           |
          |   |       * - - - + - - - *   |
          |   |       |       |       |   |
          |   |  42%  |  22%  |   6%  |   |
          |   |       |       |       |   |
          |   * - - - + - - - *       |   |
          |           |            AS |   |
          |   30%     * - - - - - - - *   |
          |                               |
          * - - - - - - - - - - - - - - - *


    b )What is the probability a randomly chosen car had neither CD nor AS?
    Look at your Venn diagram . . . It is 30%.



    c) What is the probability that a car had a CD but not an AS?

    From the diagram: . P(CD \wedge \overline{AS}) \:=\:42\%




    d) What is the probability a car with an AS had a CD?
    This one seems to be a Conditional Probability problem.

    Given that the car has an AS, what is the probability that it has a CD?

    P(\text{CD } |\text{ AS}) \:=\:\frac{0.22}{0.28} \:=\:\frac{11}{14} \:\approx\:78.6\%




    d) Are having a CD and an AS disjoint events?
    Are they independent? Explain.

    My thoughts:

    They are not independent because: . P(\text{AS}\wedge\text{CD}) \:\neq \;P(AS)\cdot P(CD)

    They are not disjoint because: . P(AS \wedge CD) \:\neq \:0
    Good!

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