Question

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

Explanation:

Step1: Recall the property of complementary events

The sum of probabilities of complementary events is \(1\).

Step2: Check each pair

• For \(\frac{2}{5}\) and \(\frac{3}{5}\): \(\frac{2}{5}+\frac{3}{5}=\frac{2 + 3}{5}=1\)
• For \(10\%\) and \(80\%\): \(10\%+80\%=90\%=0.9

eq1\)

• For \(\frac{1}{7}\) and \(\frac{2}{7}\): \(\frac{1}{7}+\frac{2}{7}=\frac{1+2}{7}=\frac{3}{7}

eq1\)

• For \(28\%\) and \(82\%\): \(28\%+82\%=110\% = 1.1

eq1\)

Answer:

\(\frac{2}{5}\) and \(\frac{3}{5}\)