On New Year's Eve, the probability of a person driving while intoxicated or having an accident is 0.38 . If the probability of driving while intoxicated is 0.32 and the probability of having a driving accident is 0.12 , find the probability of a person having a driving accident while intoxicated. The probability of a person having a driving accident while intoxicated is (Type an integer or a decimal.)

Step 1 ：We are given that the probability of a person driving while intoxicated or having an accident on New Year's Eve is 0.38, the probability of driving while intoxicated is 0.32, and the probability of having a driving accident is 0.12. We are asked to find the probability of a person having a driving accident while intoxicated.

Step 2 ：We can use the formula for conditional probability to solve this problem. The formula for conditional probability is \(P(A \text{ and } B) = P(A) \times P(B|A)\), where \(P(A \text{ and } B)\) is the probability of event A and event B happening together, \(P(A)\) is the probability of event A, and \(P(B|A)\) is the probability of event B given that event A has occurred.

Step 3 ：In this case, event A is a person driving while intoxicated and event B is a person having a driving accident. We are given \(P(A \text{ and } B)\), \(P(A)\), and \(P(B)\), and we need to find \(P(B|A)\), which is the probability of a person having a driving accident given that they are intoxicated.

Step 4 ：However, when we calculate \(P(B|A)\) using the given probabilities, we get a value greater than 1, which is not possible because the probability of an event cannot be greater than 1. This suggests that there might be a mistake in the given probabilities or in the interpretation of the problem.

Step 5 ：The sum of the individual probabilities (\(P(A)\) and \(P(B)\)) is greater than the joint probability (\(P(A \text{ and } B)\)), which is not possible in probability theory. This suggests that the events are not independent, and the joint probability should be calculated differently.

Step 6 ：After correcting the joint probability, we find that \(P(B|A)\) is 0.1875.

Step 7 ：Final Answer: The probability of a person having a driving accident while intoxicated is \(\boxed{0.1875}\).