Question

Budget rental cars cheap rentals has nothing but budget cars for rental. the probability that a car has air conditioning is 0.5, and the probability that a car has a cd player is 0.37. the probability that a car has both air conditioning and a cd player is 0.06. what is the probability that a randomly selected car has neither air conditioning nor a cd player?

Answer 1

The probability that a randomly selected car has neither air conditioning nor a CD player is 0.19.

Step-by-step explanation:

To find the probability that a randomly selected car has neither air conditioning nor a CD player, we can subtract the probability that a car has either air conditioning or a CD player, or both, from 1. This is because the sum of the probabilities of mutually exclusive events must equal 1.

The probability that a car has either air conditioning or a CD player, or both, is equal to the sum of the individual probabilities minus the probability that a car has both air conditioning and a CD player:

P(A or B) = P(A) + P(B) - P(A and B)

Using the given information:

P(A or B) = 0.5 + 0.37 - 0.06 = 0.81

Therefore, the probability that a randomly selected car has neither air conditioning nor a CD player is:

P(neither A nor B) = 1 - P(A or B) = 1 - 0.81 = 0.19.