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: .$\displaystyle P(CD \wedge \overline{AS}) \:=\:42\%$

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?

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

d) Are having a CD and an AS disjoint events?

Are they independent? Explain.

My thoughts:

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

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