Do The Math
An actuary studying the insurance preferences of automobile owners makes the following conclusions:
- An automobile owner is twice as likely to purchase collision coverage as disability coverage.
- The event that an automobile owner purchases collision coverage is independent of the event that he or she purchases disability coverage.
- The probability that an automobile owner purchases both collision and disability coverages is 0.15.
What is the probability that an automobile owner purchases neither collision nor disability coverage?
- C = Event that a policyholder buys collision coverage
D = Event that a policyholder buys disability coverage
Then we are given that
By the independence of C and D, it therefore follows that
Now the independence of C and D also implies the independence of CC and DC. As a result, we see that