Questions: The following is the breakdown of male patients with high blood pressure, high cholesterol, and diabetes at a medical center by age. Each condition is independent and no patient on the table has multiple conditions. - 25-29, 30-39, 40-49, 50-59, 60+ - High Blood Pressure: 0.01, 0.04, 0.05, 0.08, 0.22 - High Cholesterol: 0.02, 0.05, 0.08, 0.09, 0.10 - Diabetes: 0.01, 0.05, 0.05, 0.08, 0.07 What is the probability a patient does not have diabetes?

Solution Steps

To find the probability that a patient does not have diabetes, we need to calculate the complement of the probability that a patient has diabetes. This can be done by summing the probabilities of having diabetes across all age groups and then subtracting this sum from 1.

The probabilities of having diabetes in each age group are given as: \[ \begin{align_} P(D_{25-29}) &= 0.01 \\ P(D_{30-39}) &= 0.05 \\ P(D_{40-49}) &= 0.05 \\ P(D_{50-59}) &= 0.08 \\ P(D_{60+}) &= 0.07 \\ \end{align_} \]

Sum the probabilities of having diabetes across all age groups: \[ P(D) = P(D_{25-29}) + P(D_{30-39}) + P(D_{40-49}) + P(D_{50-59}) + P(D_{60+}) \] \[ P(D) = 0.01 + 0.05 + 0.05 + 0.08 + 0.07 = 0.26 \]

The probability of not having diabetes is the complement of the probability of having diabetes: \[ P(\neg D) = 1 - P(D) \] \[ P(\neg D) = 1 - 0.26 = 0.74 \]

Final Answer