Bayes' Theorem/Examples
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Examples of Use of Bayes' Theorem
Arbitrary Example $1$
Let box $1$ contain $10$ good screws and $2$ unslotted screws.
Let box $2$ contain $8$ good screws and $4$ unslotted screws.
Let a box be selected at random.
Let a screw chosen from that box prove to be unslotted.
What is the probability that it came from box $2$?
Arbitrary Example $2$
Suppose that, in a population, $6$ out of every $1000$ people has an illness $X$.
It is known that:
- if a person has $X$, there is a $92 \%$ probability that a blood test will be positive for $X$
- if a person does not have $X$, there is a $0 \cdotp 5 \%$ probability that a blood test will be positive for $X$.
Let a person selected at random test positive for $X$.
What is the probability that this person actually has $X$?