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Probability-Conditional Prob. and Independence

The Question is:
Suppose that each time that you buy a car, you choose between Ford and General Motors. Suppose that each time after the first, you stay with the same company with probability 2/3 and switch with probability 1/3. If you are equally likely to choose either company for your first car, what is the probability that your first and second choices will be Ford cars and your third and fourth choices will be General Motors cars?

What does all this mean?

Solution Preview

Let's look at each step in the "decision" process that will get you to the point of buying two Ford cars followed by two GM cars:

First selection -- buy a Ford car (probability 1/2)

Second selection -- buy a Ford car again (probability 2/3, of staying with the same brand). So far, ...

Solution Summary

This solution is comprised of a detailed explanation to answer what is the probability that your first and second choices will be Ford cars and your third and fourth choices will be General Motors cars.

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