Questions: Express the following probability as a simplified fraction and as a decimal. If one person is selected from the population described in the table, find the probability that the person is female, given that this person is divorced. Marital Status of a Certain Population, Ages 18 or Older, in Married Never Married Divorced Widowed Total ------------------ Male 70 48 8 2 128 Female 70 32 15 12 129 Total 140 80 23 14 257

Solution Steps

To find the probability that a person is female given that this person is divorced, we need to use conditional probability. The formula for conditional probability is:

\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]

Where:

• \( A \) is the event that the person is female.
• \( B \) is the event that the person is divorced.

From the table:

• The number of divorced females (\( A \cap B \)) is 15.
• The total number of divorced people (\( B \)) is 23.

So, the probability \( P(\text{Female}|\text{Divorced}) \) is:

\[ P(\text{Female}|\text{Divorced}) = \frac{15}{23} \]

We will express this probability as a simplified fraction and as a decimal.

Let \( A \) be the event that a person is female, and \( B \) be the event that a person is divorced. We need to find the conditional probability \( P(A|B) \).

From the provided table:

• The number of divorced females (\( A \cap B \)) is \( 15 \).
• The total number of divorced individuals (\( B \)) is \( 23 \).

Using the formula for conditional probability:

\[ P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{15}{23} \]

Calculating the decimal representation:

\[ P(A|B) \approx 0.6522 \]

Final Answer