Sport utility vehicles (SUVs), vans, and pickups are generally considered to be more prone to roll over than cars. In 1997, 24.0% of all highway fatalities involved rollovers; 15.8% of all fatalities in 1997 involved SUVs, vans, and pickups, given that the fatality involved a rollover. Given that a rollover was not involved, 5.6% of all fatalities involved SUVs, vans, and pickups (data extracted from A. Wilde Mathews, "Ford Ranger, Chevy Tracker Tilt in Test," The Wall Street Journal, July 14, 1999, p. A2). Consider the following definitions:
A = fatality involved an SUV, van or pickup
B = Fatality involved a rollover
a. Use Bayes' theorem to find the probability that a fatality involved a rollover, given that the fatality involved an SUV, a van, or a pickup.
b. Compare the result in (a) to the probability that a fatality involved a rollover and comment on whether SUVs, vans, and pickups are generally more prone to rollover accidents than other vehicles.