Question

which of the following values could represent the probabilities of complementary events?
$\frac{1}{7}$ and $\frac{2}{7}$
28% and 82%
$\frac{2}{5}$ and $\frac{3}{5}$
10% and 80%

Explanation:

Step1: Recall complementary events rule

The probabilities of complementary events sum to 1 (or 100%).

Step2: Check first option

Sum: $\frac{1}{7} + \frac{2}{7} = \frac{3}{7}
eq 1$

Step3: Check second option

Sum: $28\% + 82\% = 110\%
eq 100\%$

Step4: Check third option

Sum: $\frac{2}{5} + \frac{3}{5} = \frac{5}{5} = 1$

Step5: Check fourth option

Sum: $10\% + 80\% = 90\%
eq 100\%$

Answer:

$\frac{2}{5}$ and $\frac{3}{5}$