<h3><u>
Answer:</u></h3>
Hence, the probability of the complement of rolling a number less than 5 by using a six-sided die is:
1/3
<h3><u>
Step-by-step explanation:</u></h3>
Let A denote the event of rolling a number less than 5 in a six-sided die.
Now, we know that the Total outcomes are: 6
since, the sample space is given as: {1,2,3,4,5,6}
Also Number of favorable outcomes are: 4
since the numbers which are less than 5 are {1,2,3,4}
Now we have to find:
![P(A^c)](https://tex.z-dn.net/?f=P%28A%5Ec%29)
where P denotes the probability of an event and
denote the complement of event A.
We know that:
![P(A^c)=1-P(A)](https://tex.z-dn.net/?f=P%28A%5Ec%29%3D1-P%28A%29)
Now,
![P(A)=\dfrac{4}{6}\\\\P(A)=\dfrac{2}{3}](https://tex.z-dn.net/?f=P%28A%29%3D%5Cdfrac%7B4%7D%7B6%7D%5C%5C%5C%5CP%28A%29%3D%5Cdfrac%7B2%7D%7B3%7D)
Hence,
![P(A^c)=1-\dfrac{2}{3}\\\\P(A^c)=\dfrac{3-2}{3}\\\\P(A^c)=\dfrac{1}{3}](https://tex.z-dn.net/?f=P%28A%5Ec%29%3D1-%5Cdfrac%7B2%7D%7B3%7D%5C%5C%5C%5CP%28A%5Ec%29%3D%5Cdfrac%7B3-2%7D%7B3%7D%5C%5C%5C%5CP%28A%5Ec%29%3D%5Cdfrac%7B1%7D%7B3%7D)
Hence, the probability of the complement of rolling a number less than 5 by using a six-sided die is:
1/3