Question

The windshield wipers on the car have not been working properly. The probability that the car needs a new motor is 0.6, the probability that the car needs a new switch is 0.4, and the probability that the car needs both is 0.15. What is the probability that the car needs neither a new motor nor a new switch?

Answer 1

The probability that the car needs neither a new motor nor a new switch is 0.15

Explanation:

Here, we have a probability question to work with.

Let the probability of needing a new motor be P(M) , while the probability of needing a new switch be P(S);

First, the probability of calculating the union of the two events is;

P(M ∪ S) = P(M) + P(S) - P(M ∩ S)

From the question, we identify the following;

P(M) = 0.6, P(S) = 0.4 and P(M ∩ S) = 0.15

Let's plug these values into the equation above;

P(M ∪ S) = 0.6 + 0.4 - 0.15 = 1-0.15 = 0.85

It must be known that the probability that the car needs neither is the complement of the union

Hence, P(M ∪ S) =1 - (P(M ∪ S)') = 1 - 0.85 = 0.15