Question

The probability of an event is $\frac{8}{9}$. What is the probability of the complement of this event?

• A. $\frac{8}{9}$
• B. $\frac{1}{9}$
• C. $\frac{2}{9}$
• D. $0$

Answer 1

The correct option is B $\frac{1}{9}$

Suppose, the given event is $\text{E}$. Then its complement can be denoted as $\overline{\text{E}}$.

As per the question, the probability of the event $\text{E}$ $=\text{P(E)}=\frac{8}{9}$.

$\text{To Find:}$ Probability of complement of the event $\text{E}$, i.e., $\text{P}$$\left(\overline{\text{E}}\right)$

Complement rule states that the summation of probabilities of an event and it's complement is always equal to $1$, i.e.,
$\text{P(E)}+\text{P}$$\left(\overline{\text{E}}\right)=1$.

$\therefore \text{P}\left(\overline{\text{E}}\right)=1-\text{P(E)}=1-\frac{8}{9}=\frac{9}{9}-\frac{8}{9}$
$\Rightarrow \text{P}$$\left(\overline{\text{E}}\right)=\frac{9-8}{9}=\frac{1}{9}$

$\therefore$ The probability of complement of the event $\text{E}$ is $\frac{1}{9}$.

Hence, option (b.) is the correct answer.