Questions: Marital Status of the U.S. Population, Ages 18 or Older, in Millions If one person is selected from the population described in the table, find the probability that the person is female, given that this person never married. Never Married Married Widowed Divorced Total --------------------------------------------------------- Male 28.1 63.5 3.1 9.0 103.7 Female 23.3 63.6 10.7 12.7 110.3 Total 51.4 127.1 13.8 21.7 214.0 The probability is approximately (Round to three decimal places as needed.)

Solution Steps

To find the probability that a person is female given that this person has never married, we need to use conditional probability. The formula for conditional probability is \( P(A|B) = \frac{P(A \cap B)}{P(B)} \), where \( P(A|B) \) is the probability of event A given event B. Here, event A is the person being female, and event B is the person never married.

1. Identify the number of females who have never married.
2. Identify the total number of people who have never married.
3. Use the conditional probability formula to find the required probability.

From the data provided, we have:

• The number of females who have never married: \( 23.3 \) million.
• The total number of people who have never married (both males and females): \( 51.4 \) million.

We need to find the probability \( P(\text{Female} | \text{Never Married}) \). Using the formula for conditional probability:

\[ P(\text{Female} | \text{Never Married}) = \frac{P(\text{Female} \cap \text{Never Married})}{P(\text{Never Married})} \]

Substituting the values:

\[ P(\text{Female} | \text{Never Married}) = \frac{23.3}{51.4} \]

Calculating the above expression gives:

\[ P(\text{Female} | \text{Never Married}) \approx 0.453 \]

Rounding the result to three decimal places, we have:

\[ P(\text{Female} | \text{Never Married}) \approx 0.453 \]

Final Answer