a number of candidate interviewed recently revealed that 142 applied for admission into university of lagos ,122 for ilorin and 118 for jos ,66 had applied for lagos and ilorin ,48 for ilorin and jos and 58 for lagos and jos while 32 had applied for all three universities a. illustrate the information using venn diagram b. how many candidate were interviewed
a.
Let's represent the three universities as circles A (Lagos), B (Ilorin), and C (Jos).
From the information given:
- 66 candidates applied for both Lagos and Ilorin (A ∩ B)
- 48 candidates applied for both Ilorin and Jos (B ∩ C)
- 58 candidates applied for both Lagos and Jos (A ∩ C)
- 32 candidates applied for all three universities (A ∩ B ∩ C)
We can place these values in the appropriate sections of the Venn diagram.
b. To find out the total number of candidates interviewed, we need to calculate the total number of candidates who applied to each university and then add the number of candidates who applied to more than one university only once.
Total = Number of candidates who applied to Lagos + Number of candidates who applied to Ilorin + Number of candidates who applied to Jos - (Number of candidates who applied to both Lagos and Ilorin + Number of candidates who applied to both Ilorin and Jos + Number of candidates who applied to both Lagos and Jos) + Number of candidates who applied to all three universities
Total = 142 + 122 + 118 - (66 + 48 + 58) + 32
Total = 382 - 172 + 32
Total = 242
Therefore, a total of 242 candidates were interviewed.