Safety Insurance Company Has Compiled the Following Statistics

question 38

Short Answer

Safety Insurance Company has compiled the following statistics. For any one-year period:
P(accident | male driver under 25) = .22
P(accident | male driver over 25) = .15
P(accident | female driver under 25) = .16
P(accident | female driver over 25) = .14
The percentage of Safety's policyholders in each category is:
Male Under 25 20%
Male Over 25 40%
Female Under 25 10%
Female Over 25 30%
a. What is the probability that a randomly selected policyholder will have an accident within the next year?
b. Given that a driver has an accident, what is the probability the driver is a male over 25?
c. Given that a driver has no accident, what is the probability the driver is a female?

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Definitions:

Day of Week

Indicates one of the seven named divisions in a week, ranging from Sunday to Saturday.

Interaction Effect

In statistics, it refers to a situation in which the effect of one independent variable on a dependent variable changes depending on the level of another independent variable.

Marginal Mean

The mean of the subset of observations that contribute to the marginal total, providing insight into specific group effects within a larger dataset.

Factorial Designs

Experimental designs used to evaluate the effects of two or more factors by varying them simultaneously and systematically.