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.
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
Hello, rice4lifelegit!
I assume that part (a) was to draw the Venn diagram.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.Code:* - - - - - - - - - - - - - - - * | | | * - - - - - - - * | | | CD | | | | * - - - + - - - * | | | | | | | | | 42% | 22% | 6% | | | | | | | | | * - - - + - - - * | | | | AS | | | 30% * - - - - - - - * | | | * - - - - - - - - - - - - - - - *
Look at your Venn diagram . . . It is 30%.b )What is the probability a randomly chosen car had neither CD nor AS?
c) What is the probability that a car had a CD but not an AS?
From the diagram: .
This one seems to be a Conditional Probability problem.d) What is the probability a car with an AS had a CD?
Given that the car has an AS, what is the probability that it has a CD?
Good!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: .