let A denote the event that the chosen individual is female and B denote the event that the chosen individual is over 50 years old.

Given : Town consists of 6000 people, 1200 are over 50 years old, and 2000 are females

To find : Probability that a randomly chosen individual from the town is either female or over 50 years = P(A or B) 

The formula used : Probability = 

  = \(\frac{favourable\,number\,of\,outcomes}{Total\,no.of\,outcomes}\)

P(A or B) = P(A) + P(B) - P(A and B)

For the event A , 

There are 2000 females present in a town of 6000 people

Favourable number of outcomes = 2000 

Total number of outcomes = 6000

P(A) = \(\frac{2000}{6000}\) = \(\frac{1}{3}\)

For the event B, 

There are 1200 are over 50 years of age in a town of 6000 people

Favourable number of outcomes = 1200 

Total number of outcomes = 6000 

P(A) = \(\frac{2000}{6000}\) = \(\frac{1}{5}\)

30% of the females are over 50 years

For the event A and B, 

\(\frac{30}{100}\times2000 = 600\) females are over 50

Favourable number of outcomes = 600

P(A and B) = \(\frac{600}{6000}\) = \(\frac{1}{10}\)

= P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = \(\frac{1}{3}+\frac{1}{5}+\frac{1}{10}\)

P(A or B) = \(\frac{10+6-3}{30}\) = \(\frac{13}{30}\)

P(A or B) =  \(\frac{13}{30}\) 

The probability that a randomly chosen individual from the town is either female or over 50 years = P(A or B) =  \(\frac{13}{30}\)