[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