Consider all cars that are involved in an accident and assume that all cars are classified as either small or large. The probability that a small car is involved an accident is .2 if a small car is involved in an accident, the probabbility that there was fatality in that accident is .12. if a large car is involved in an accident, then the probability that there was a fatality is .05.

what is the probability that at large car is involved?
What is the probability of having in an accident in a small car and the accident is fatality?
If an accident is a fatality, what is the probability that a small car was involved?
Does the event of having a fatality accident depend on the car size?

To find the probability that a large car is involved in an accident, you need to know the probability of a small car being involved in an accident and the probability of a large car being involved in an accident. From the given information, we know that the probability of a small car being involved in an accident is 0.2. Therefore, the probability of a large car being involved in an accident would be the complement of this probability, which is 1 - 0.2 = 0.8.

To find the probability of having an accident in a small car that results in a fatality, you need to multiply the probabilities of these two events occurring together. From the given information, the probability of a fatality given a small car accident is 0.12. Therefore, the probability of having an accident in a small car that results in a fatality is 0.2 * 0.12 = 0.024.

To find the probability that a small car was involved given that the accident is a fatality, you can use Bayes' theorem. The theorem states that P(A|B) = (P(B|A) * P(A)) / P(B), where A and B are events. In this case, A represents a small car being involved and B represents a fatality. Using the given information, P(A) = 0.2, P(B|A) = 0.12, and P(B) can be calculated by considering both small and large cars. P(B) = P(B|A) * P(A) + P(B|not A) * P(not A) = 0.12 * 0.2 + 0.05 * 0.8 = 0.024 + 0.04 = 0.064. Therefore, P(A|B) = (0.12 * 0.2) / 0.064 = 0.375.

Lastly, the event of having a fatality accident does depend on the car size. From the given information, we can see that the probability of a fatality is different for small cars (0.12) and large cars (0.05). Therefore, the occurrence of a fatality is influenced by the size of the involved car.