Question

Emma is a darts player. She hit the target seven times out of eighteen throws. What is the experimental probability that Emma's next throw will not hit the target?

• A. $\frac{7}{18}$
• B. $\frac{11}{18}$
• C. $\frac{13}{18}$
• D. $\frac{18}{11}$

Answer 1

The correct option is B $\frac{11}{18}$

$\underset{–}{\text{Given}:}$
Emma hits the target $7$ times out of $18$ throws

Let hitting the target is an event, $E$

Thus not hitting the target is the complement event of event $E$, i.e., the not hitting the target can be denoted by $\overline{E}$

Total number of possible outcomes
$=$ Total number of throws
$=20$

Number of favorable outcomes of event, $E$
$=$ Number of times the target is hitted
$=7$

$\therefore \text{P}\left(E\right)=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

$\Rightarrow \text{P}\left(E\right)=\frac{7}{18}$

Now, according to complement rule of probability,
$\text{P}\left(\overline{E}\right)=1-\text{P}\left(E\right)$

$\Rightarrow \text{P}\left(\overline{E}\right)=1-\frac{7}{18}=\frac{18-7}{18}=\frac{11}{18}$

Hence, the probability that Emma's next throw will not hit the target is $\frac{11}{18}.$

Therefore, option (b.) is the correct choice.