3.96 An insurance company estimated that 30% of all automobile accidents were partly caused by weather conditions and that 20% of all automobile accidents involved bodily injury. Further, of those accidents that involved bodily injury, 40% were partly caused by weather conditions.

a. What is the probability that a randomly chosen accident both was partly caused by weather conditions and involved bodily injury?

b. Are the events “partly caused by weather conditions”

and “involved bodily injury” independent?

c. If a randomly chosen accident was partly caused by weather conditions, what is the probability that it involved bodily injury?

d. What is the probability that a randomly chosen accident both was not partly caused by weather conditions and did not involve bodily injury?