# 1. A blood test is 90% effective in detecting a disease. It also falsely diagnoses that a healthy…

1. A blood test is 90% effective in detecting a
disease. It also falsely diagnoses that a healthy person has the disease 3% of
the time. If 10% of those tested have the disease, what is the probability that
a person who tests positive will actually have the disease?

2. Suppose an automobile insurance company
classifies a driver as good, average, or bad. Of all their insured drivers, 25%
are classified good, 50% are average, and 25% are bad. Suppose for the coming
year, a good driver has a 5% chance of having an accident, and an average
driver has 15% chance of having an accident, and a bad

1. A blood test is 90% effective in detecting a
disease. It also falsely diagnoses that a healthy person has the disease 3% of
the time. If 10% of those tested have the disease, what is the probability that
a person who tests positive will actually have the disease?

2. Suppose an automobile insurance company
classifies a driver as good, average, or bad. Of all their insured drivers, 25%
are classified good, 50% are average, and 25% are bad. Suppose for the coming
year, a good driver has a 5% chance of having an accident, and an average
driver has 15% chance of having an accident, and a bad driver has a 25% chance.
If you had an accident in the past year what is the probability that you are a
good driver?

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