Concept explainers
a.
Compute the probability that selected patient is a woman.
a.
Answer to Problem 10RE
The probability that selected patient is a woman is 0.4035.
Explanation of Solution
Calculation:
It is given that 644,404 patients were hospitalized for heart attack. The table provides idea about number of male and female patients hospitalized in each age group.
The probability of the event A can be obtained by the formula:
Here, event A denotes that selected patient is a woman. Among the 644,404 patients, 260,005 of them are woman.
Substitute 260,005 for “number of outcomes in A” and 644,404 for “Number of outcomes in
Therefore,
Thus, the probability that selected patient is a woman is 0.4035.
b.
Compute the probability that selected patient is aged 45-64.
b.
Answer to Problem 10RE
The probability that selected patient is aged 45-64 is 0.3647.
Explanation of Solution
Calculation:
Event B denotes that selected patient is aged 45-64. Among the 644,404 patients, 235,006 of them are woman.
Substitute 235,006 for “number of outcomes in B” and 644,404 for “Number of outcomes in sample space” in the probability formula.
Therefore,
Thus, the probability that selected patient is aged 45-64 is 0.3647.
c.
Compute the probability that selected patient is a woman and aged 45-64.
c.
Answer to Problem 10RE
The probability that selected patient is a woman and aged 45-64 is 0.1066.
Explanation of Solution
Calculation:
Event A denotes that selected patient is a woman and event B denotes that selected patient is aged 45-64. Event ‘A and B’ denote that selected patient is a woman and aged 45-64.
Among the 644,404 patients, 68,666 of them are woman and aged 45-64.
Substitute 68,666 for “number of outcomes in ‘A and B’” and 644,404 for “Number of outcomes in sample space” in the probability formula.
Therefore,
Thus, the probability that selected patient is a woman and aged 45-64 is 0.1066.
d.
Compute the probability that selected patient is a woman or aged 45-64.
d.
Answer to Problem 10RE
The probability that selected patient is a woman or aged 45-64 is 0.6616.
Explanation of Solution
Calculation:
Event A denotes that selected patient is a woman and event B denotes that selected patient is aged 45-64. Event ‘A and B’ denote that selected patient is a woman and aged 45-64.
The probability that selected patient is a woman or aged 45-64 can be expressed as,
General
For any two events A and B the general addition rule states that
From parts (a), (b), and (c),
Substitute these values in the general addition rule.
Therefore,
Thus, the probability that selected patient is a woman or aged 45-64 is 0.6616.
e.
Compute the probability that selected patient is a woman given that the patient is aged 45-64.
e.
Answer to Problem 10RE
The probability that selected patient is a woman given that the patient is aged 45-64 is 0.2922.
Explanation of Solution
Calculation:
The formula for conditional probability is given by:
From part (b),
From part (c),
Substitute these values in the formula for conditional probability.
Therefore,
Thus, the probability that selected patient is a woman given that the patient is aged 45-64 is 0.2922.
f.
Compute the probability that selected patient is aged 45-64 given that the patient is a woman.
f.
Answer to Problem 10RE
The probability that selected patient is aged 45-64 given that the patient is a woman is 0.2641.
Explanation of Solution
Calculation:
The formula for conditional probability is given by:
From part (a),
From part (c),
Substitute these values in the formula for conditional probability.
Therefore,
Thus, the probability that selected patient is aged 45-64 given that the patient is a woman is 0.2641.
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ESSENTIAL STATISTICS W/CONNECT