Question

if the probability of an event is 2/7, what must be the probability of its complement?

Explanation:

Step1: Recall the formula for complementary events

The probability of an event \(P(E)\) and the probability of its complement \(P(\overline{E})\) satisfy the formula \(P(E)+P(\overline{E}) = 1\).

Step2: Substitute the given probability into the formula

Given \(P(E)=\frac{2}{7}\), we substitute into \(P(\overline{E})=1 - P(E)\). So \(P(\overline{E})=1-\frac{2}{7}\).

Step3: Calculate the value

\(1-\frac{2}{7}=\frac{7}{7}-\frac{2}{7}=\frac{7 - 2}{7}=\frac{5}{7}\)

Answer:

\(\frac{5}{7}\)