Probabilities are used to determine the chances of an event.
The probability that Bella’s two choices will be picked is 1/231
The parameters are given as:
[tex]\mathbf{n = 22}[/tex] -- number of students
[tex]\mathbf{r = 2}[/tex] --- Bella's selection.
Each student in the class have an equal chance.
So, the probability of selecting a student is:
[tex]\mathbf{Pr = \frac 1{22}}[/tex]
The probability that Bella's two choices are picked is:
[tex]\mathbf{Pr = P(First\ and\ Second)\ or\ P(Second\ and\ First)}[/tex]
So, we have:
[tex]\mathbf{Pr = \frac{1}{22} \times \frac{1}{22 - 1} + \frac{1}{22} \times \frac{1}{22 -1}}[/tex]
NB: 1 is subtracted, because no students can be selected more than once
So, we have:
[tex]\mathbf{Pr = \frac{1}{22} \times \frac{1}{21} + \frac{1}{22} \times \frac{1}{21}}[/tex]
[tex]\mathbf{Pr = \frac{1}{462} + \frac{1}{462}}[/tex]
Take LCM
[tex]\mathbf{Pr = \frac{1 +1}{462}}[/tex]
[tex]\mathbf{Pr = \frac{2}{462}}[/tex]
Simplify
[tex]\mathbf{Pr = \frac{1}{231}}[/tex]
Hence, the probability that Bella’s two choices will be picked is 1/231
Read more about probabilities at:
https://brainly.com/question/11234923
