Question

if the probability of an event is (\frac{2}{7}), what must be the probability of its complement? (\bigcirc \frac{1}{7}) (\bigcirc \frac{2}{7}) (\bigcirc \frac{4}{7}) (\bigcirc \frac{5}{7})

Explanation:

Step1: Recall the complement rule

The probability of an event $A$ and its complement $\overline{A}$ satisfies $P(A)+P(\overline{A}) = 1$.

Step2: Substitute the given probability

Given $P(A)=\frac{2}{7}$, we solve for $P(\overline{A})$:
$P(\overline{A})=1 - P(A)$
$P(\overline{A}) = 1-\frac{2}{7}$

Step3: Calculate the result

$1=\frac{7}{7}$, so $\frac{7}{7}-\frac{2}{7}=\frac{7 - 2}{7}=\frac{5}{7}$.

Answer:

$\frac{5}{7}$