4.2 The Progressive Corporation offers its automobile insurance customers the opportunity to participate in its Snapshot program. Snapshot is a small box that is plugged into the car and records the number of miles driven, the number of miles driven between midnight and 4 a.m., and whether the driver uses hard or soft braking. The program is voluntary; customers do not have to participate. Suppose that 80 percent of Progressive’s customers are safe drivers and 20 percent are risky drivers.

a. Initially, the program offered discounts to drivers determined to be safe. The program did not penalize risky drivers. What do you think were the approximate percentages of safe drivers and risky drivers that participated in the Snapshot program?

Explain your answer.

b. Recently, Progressive changed the details of the Snapshot program so that Progressive gives drivers determined to be safe a discount and hits drivers determined to be risky with a surcharge. How do you think this change affected the percentages of safe drivers and risky drivers participating in the Snapshot program?