Concept explainers
a.
Check whether
Explain the answer.
a.
Answer to Problem 10P
Events
Explanation of Solution
Calculation:
The prior probabilities for the events
The values of
Mutually exclusive events:
Two or more events are said to be mutually exclusive if they have no element in common. For mutually exclusive events,
Here,
b.
Compute the probability values
b.
Answer to Problem 10P
The probabilities are:
Explanation of Solution
Calculation:
The Multiplication Rule:
For any two events A and B, the multiplication rule states that
Required probabilities are:
Here,
Substitute these values in the above formula.
Therefore,
Thus,
Therefore,
Thus,
c.
Compute the probability value
c.
Answer to Problem 10P
The probability value is,
Explanation of Solution
Calculation:
The probability of the
From part (b),
Substitute these values in the above formula.
Therefore,
Thus,
d.
Compute
d.
Answer to Problem 10P
The probability values are:
Explanation of Solution
Calculation:
Bayes Theorem (Two-Event Case):
From part (b),
From part (c),
Substitute these values in the Bayes’ theorem.
Therefore,
Thus,
Thus,
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