Thread: [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

Here is the setup: .
So .
That is the probability of a car having at least one of the systems.
So is the probability of a can having neither.

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: .

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?

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

My thoughts:

They are not independent because: .

They are not disjoint because: .

Good!