To determine which pair does not represent the probabilities of complementary events, we need to understand that two events are complementary if the sum of their probabilities is equal to 1.
Let's examine each pair one by one:
1. [tex]\(\frac{4}{7}\)[/tex] and [tex]\(\frac{3}{7}\)[/tex]:
[tex]\[
\frac{4}{7} + \frac{3}{7} = \frac{7}{7} = 1
\][/tex]
These events are complementary.
2. [tex]\(16\%\)[/tex] and [tex]\(84\%\)[/tex]:
[tex]\[
16\% + 84\% = 100\% = 1
\][/tex]
These events are complementary.
3. [tex]\(0.25\)[/tex] and [tex]\(0.50\)[/tex]:
[tex]\[
0.25 + 0.50 = 0.75
\][/tex]
These events are not complementary since the sum is not equal to 1.
4. [tex]\(0\)[/tex] and [tex]\(1\)[/tex]:
[tex]\[
0 + 1 = 1
\][/tex]
These events are complementary.
From our examination, the third pair, 0.25 and 0.50, does not sum to 1 and therefore does not represent the probabilities of complementary events.
Thus, the pair [tex]\(\{0.25, 0.50\}\)[/tex] does not represent complementary events.
