Question

in a town of 6000 people , 1200 are over 50 years old and 2000 are females.it is known that 30% of the females are over 50 years. What is the probability that the randomly chosen individual from the town is either female or 50 years old??

Answer 1

 you need to exclude the overlap first ( females who are over 50). 
You can find this by taking 30% of 2000 
2000*0.3 = 600 

Now add the over 50's, the females, and subtract the overlap and divide by the total population 
(1200+2000-600)/6000 
2600/6000 
26/60 
13/30 

Answer 2

Total population = 6000

2000 are females
30% of 2000 females are over 50 years of age.
30% of 2000 = (30/100)*2000
                     = 600

1200 of the total population are over 50.
600 old females means 600 old males.

Probability= (No. of females + No. of people older than 50 years of age - No.                      of old females)/ Total population
                 =(2000 + 1200 - 600) / 6000
                 = 2600/6000
                 = 26/60
                 = 13/30

Hence the probability of choosing either female or a 50 year old is 13/30

Thankyou