The windshield wipers on a car have not been working properly. The probability that the car needs a new motor is 0.55 , the probability that the car needs a new switch is 0.45 , and the probability that the car needs both is 0.2 . What is the probability that the car needs neither a new motor nor a new switch?

The probability that the car requires needs neither a new motor nor a new switch is $\square$.
(Type an integer or a decimal.)

Step 1 ：The problem is asking for the probability that the car needs neither a new motor nor a new switch. This is equivalent to the complement of the event that the car needs either a new motor or a new switch.

Step 2 ：The probability of the union of two events A and B is given by P(A U B) = P(A) + P(B) - P(A ∩ B). Here, event A is the car needing a new motor, event B is the car needing a new switch, and event A ∩ B is the car needing both a new motor and a new switch.

Step 3 ：We can calculate the probability of the car needing either a new motor or a new switch using the given probabilities, and then subtract this from 1 to find the probability of the car needing neither.

Step 4 ：Let P_A = 0.55, P_B = 0.45, P_A_and_B = 0.2

Step 5 ：Calculate P_A_or_B = P_A + P_B - P_A_and_B = 0.55 + 0.45 - 0.2 = 0.8

Step 6 ：Calculate P_neither = 1 - P_A_or_B = 1 - 0.8 = 0.2

Step 7 ：Final Answer: The probability that the car requires needs neither a new motor nor a new switch is \(\boxed{0.2}\)