An insurance company estimated that 30% of all automobile accidents were partly caused by weather conditions, and that 20% of all 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 and involved bodily injury?
b. What is the probability that a randomly chosen accident was either partly caused by weather or involved bodily injury or both?
c. What is the probability that a randomly chosen accident both was not partly caused by weather and did not involve bodily injury?