Question

John rolls a die. What is the likelihood of not rolling $6$?

• A. $\frac{1}{6}$
• B. $\frac{3}{6}$
• C. $\frac{5}{6}$
• D. None of the above

Answer 1

The correct option is C $\frac{5}{6}$

As we know, rolling $6$ and not rolling $6$ on a fair die are complements of each other.

Hence,
$\text{P(rolling 6)}+\text{P(not rolling 6)}=1$

$\Rightarrow \text{P(not rolling 6)}=1-\text{P(rolling 6)}$

Let's find the $\text{P(rolling 6)}$

Given, John rolls a die, thus the $\text{Sample Space}=\{1,2,3,4,5,6\}$
$\therefore$ Total number of outcomes $=6$
Number of favorable outcomes to rolling $6=1$

$\text{P(rolling 6)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{1}{6}$

So,
$\text{P(not rolling 6)}=1-\frac{1}{6}$

$\Rightarrow \text{P(not rolling 6)}=\frac{6}{6}-\frac{1}{6}$

$\Rightarrow \text{P(not rolling 6)}=\frac{6-1}{6}=\frac{5}{6}$

$\therefore$ The likelihood of not rolling $6$ on a fair die is $\frac{5}{6}$.

Hence, option (c.) is the correct choice.