1) 1/8
2) 1/2
Step-by-step explanation:
1)
First of all, we notice that the spinner is divided into 8 sections of equal size.
So the number of sections is
n = 8
Secondly, we note that each section has the same size: this means that the probability of the spinner landing on each section is the same.
The probabilty of a certain event A to occur is given by
![p(A)=\frac{a}{n}](https://tex.z-dn.net/?f=p%28A%29%3D%5Cfrac%7Ba%7D%7Bn%7D)
where
a is the number of successfull outcomes (in which A occurs)
n is the total number of possible outcomes
Here we want to find
= probability that the spinner lands on section 7
Here we have:
(only 1 outcome is successfull: the one in which the spinner lands on section 7)
![n=8](https://tex.z-dn.net/?f=n%3D8)
Therefore, the probability is
![p(7)=\frac{1}{8}](https://tex.z-dn.net/?f=p%287%29%3D%5Cfrac%7B1%7D%7B8%7D)
2)
Here we want to find the probability that the spinner lands on an even numbered section.
As before, the total number of possible outcomes his:
![n=8](https://tex.z-dn.net/?f=n%3D8)
which corresponds to: 1, 2, 3, 4, 5, 6, 7, 8
The even-numbered sections are:
2, 4, 6, 8
So, the number of successfull outcomes is
![a=4](https://tex.z-dn.net/?f=a%3D4)
Because there are only 4 even-numbered sections.
Therefore, the probability that the spinner lands on an even numbered section is:
![p(e)=\frac{a}{n}=\frac{4}{8}=\frac{1}{2}](https://tex.z-dn.net/?f=p%28e%29%3D%5Cfrac%7Ba%7D%7Bn%7D%3D%5Cfrac%7B4%7D%7B8%7D%3D%5Cfrac%7B1%7D%7B2%7D)