To determine which pair does not represent the probabilities of complementary events, we should check if the sum of each pair equals 1. Complementary probabilities are two events whose probabilities add up to 1.
Let's check each pair step by step:
1. First pair: [tex]$\frac{4}{7}$[/tex] and [tex]$\frac{3}{7}$[/tex]
- Sum: [tex]\(\frac{4}{7} + \frac{3}{7} = \frac{4 + 3}{7} = \frac{7}{7} = 1\)[/tex]
- Conclusion: These probabilities are complementary since their sum is 1.
2. Second pair: 16% and 84%
- Convert percentages to decimals: 16% = 0.16 and 84% = 0.84
- Sum: [tex]\(0.16 + 0.84 = 1.00\)[/tex]
- Conclusion: These probabilities are complementary since their sum is 1.
3. Third pair: 0.25 and 0.50
- Sum: [tex]\(0.25 + 0.50 = 0.75\)[/tex]
- Conclusion: These probabilities are not complementary since their sum is 0.75, which is not equal to 1.
4. Fourth pair: 0 and 1
- Sum: [tex]\(0 + 1 = 1\)[/tex]
- Conclusion: These probabilities are complementary since their sum is 1.
Upon examining each pair, we find that the third pair ([tex]\(0.25\)[/tex] and [tex]\(0.50\)[/tex]) does not sum up to 1 and, therefore, does not represent complementary probabilities.
Thus, the pair that does not represent the probabilities of complementary events is:
[tex]$ \boxed{0.25 \text{ and } 0.50} $[/tex]
