Correct Option (4)

To determine the fraction of females who are single, we can assume a total population for calculation purposes. Let the total number of persons in the group be 100 units.

Number of males = 70% of 100 = 70 units.
Number of females = 30% of 100 = 30 units.
Total number of married persons = 30% of 100 = 30 units.

It is given that two-sevenths of the males are married.

Number of married males = $\frac{2}{7} \times 70 = 20$ units.

The total number of married persons is 30 units. Since 20 units are married males, the remaining married individuals must be females.

Number of married females = Total married persons - Married males = $30 - 20 = 10$ units.

To find the number of single females, subtract the married females from the total number of females.

Number of single females = Total females - Married females = $30 - 10 = 20$ units.

The question asks for the fraction of females that is single. This is calculated as the ratio of single females to the total number of females.

Fraction of females that is single = $\frac{Number of single females}{Total number of females} = \frac{20}{30} = \frac{2}{3}$ .

Incorrect Options:

Options 1 (2/7), 2 (1/3), and 3 (3/7) are incorrect as they do not align with the derived fraction of single females, which is $\frac{2}{3}$ .