Recently a census was taken on space station Gamma. Of the 100 residents interviewed, 75 traced their ancestry to the planet Omicron, 85 traced their ancestry to the planet Omega and 60 residents traced their ancestry to both planets. How many residents had ancestors from ONLY Omicron and how many residents had ancestors from ONLY Omega?
number(Omicron only) = 75-60 = 15
number(Omega only) = 85-60 = 25
To determine the number of residents with ancestors from ONLY Omicron and the number of residents with ancestors from ONLY Omega, we can use a method called the Inclusion-Exclusion Principle.
Let's break down the given information:
- Number of residents from Omicron (in either case, only Omicron or both Omicron and Omega): 75
- Number of residents from Omega (in either case, only Omega or both Omicron and Omega): 85
- Number of residents from both Omicron and Omega: 60
To find the number of residents with ancestors from ONLY Omicron, we need to subtract the number of residents with ancestors from both planets from the total number of residents traced to Omicron:
Residents with ONLY Omicron = Total residents traced to Omicron - Residents with both Omicron and Omega
Residents with ONLY Omicron = 75 - 60
Residents with ONLY Omicron = 15
Similarly, to find the number of residents with ancestors from ONLY Omega, we need to subtract the number of residents with ancestors from both planets from the total number of residents traced to Omega:
Residents with ONLY Omega = Total residents traced to Omega - Residents with both Omicron and Omega
Residents with ONLY Omega = 85 - 60
Residents with ONLY Omega = 25
So, there are 15 residents with ancestors from ONLY Omicron and 25 residents with ancestors from ONLY Omega on the space station Gamma.