Title: A survey of local car dealers revealed that 64% of all cars sold last month had CD players, 28% had ...
Post by: Lighting2551 on Aug 31, 2019
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.
a. What is the probability one of these cars selected at random had neither a CD player nor an alarm system?
b. What is the probability that a car had a CD player unprotected by an alarm system?
c. What is the probability a car with an alarm system had a CD player?
d. Are having a CD player and an alarm system disjoint events? Explain.
a. What is the probability one of these cars selected at random had neither a CD player nor an alarm system?
b. What is the probability that a car had a CD player unprotected by an alarm system?
c. What is the probability a car with an alarm system had a CD player?
d. Are having a CD player and an alarm system disjoint events? Explain.
Title: A survey of local car dealers revealed that 64% of all cars sold last month had CD players, 28% had ...
Post by: Nikki_LYNN on Aug 31, 2019
a. P(CD ∪ A) = P(CD) + P(A) - P(CD ∩ A) = 0.64 + 0.28 - 0.22 = 0.70,
so P(neither) = 1 - 0.70 = 0.30
Or, using the Venn diagram below, 30%
b. P(CD ∩ AC) = 0.64 - 0.22 = 0.42
c. P(CD
) = 
= 
≈ 0.786
d. No. P(CD ∩ A) = 0.22. If they were disjoint, the probability of a car having both features would be 0.
so P(neither) = 1 - 0.70 = 0.30
Or, using the Venn diagram below, 30%
b. P(CD ∩ AC) = 0.64 - 0.22 = 0.42
c. P(CD
) = = ≈ 0.786d. No. P(CD ∩ A) = 0.22. If they were disjoint, the probability of a car having both features would be 0.