Answer :
To find the probability that a randomly selected person has never married, given that the person is a woman, let's follow these steps:
1. Identify the relevant values from the table:
- Number of women who have never married: 29
- Total number of women: 106
2. Set up the probability:
The probability [tex]\( P(\text{Never Married} | \text{Female}) \)[/tex] is the number of women who have never married divided by the total number of women.
3. Write the probability as a fraction:
[tex]\[ P(\text{Never Married} | \text{Female}) = \frac{\text{Number of women who never married}}{\text{Total number of women}} = \frac{29}{106} \][/tex]
4. Simplify the fraction (if possible):
- In this case, the fraction [tex]\(\frac{29}{106}\)[/tex] is already in its simplest form because 29 and 106 have no common factors other than 1.
5. Express the probability as a decimal:
To convert the fraction to a decimal, divide 29 by 106:
[tex]\[ \frac{29}{106} \approx 0.27358490566037735 \][/tex]
Thus, the probability that a randomly selected person has never married, given that the person is a woman, can be expressed as:
- Fraction: [tex]\(\frac{29}{106}\)[/tex]
- Decimal: [tex]\(0.27358490566037735\)[/tex]
Therefore, the simplified fraction representing the probability is [tex]\( \boxed{\frac{29}{106}} \)[/tex].
1. Identify the relevant values from the table:
- Number of women who have never married: 29
- Total number of women: 106
2. Set up the probability:
The probability [tex]\( P(\text{Never Married} | \text{Female}) \)[/tex] is the number of women who have never married divided by the total number of women.
3. Write the probability as a fraction:
[tex]\[ P(\text{Never Married} | \text{Female}) = \frac{\text{Number of women who never married}}{\text{Total number of women}} = \frac{29}{106} \][/tex]
4. Simplify the fraction (if possible):
- In this case, the fraction [tex]\(\frac{29}{106}\)[/tex] is already in its simplest form because 29 and 106 have no common factors other than 1.
5. Express the probability as a decimal:
To convert the fraction to a decimal, divide 29 by 106:
[tex]\[ \frac{29}{106} \approx 0.27358490566037735 \][/tex]
Thus, the probability that a randomly selected person has never married, given that the person is a woman, can be expressed as:
- Fraction: [tex]\(\frac{29}{106}\)[/tex]
- Decimal: [tex]\(0.27358490566037735\)[/tex]
Therefore, the simplified fraction representing the probability is [tex]\( \boxed{\frac{29}{106}} \)[/tex].
