The probability that an 8th grader will be selected from selection of a student for the considered case is 1/3
How to calculate the probability of an event?
Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
For this case, it is given that:
- Twelve students have an equally likely chance of being selected in a drawing at school.
- Out of those 12, number of 7th grader = 8
- Out of those 12, number of 8th grader = 4
To find: Probability that an 8th grader will be selected
Take an event E as:
E = event of selecting an 8th grader.
Then, as there are 4 such students, so event E can be done in 4 ways.
Total students are 12, so selecting a student (whether E occurs or not) is do-able in 12 ways.
As all the students are equally likely, we can use the above definition of probability of an event E, and therefore, we get:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{4}{12} = \dfrac{1}{3}[/tex]
Thus, the probability that an 8th grader will be selected from selection of a student for the considered case is 1/3
Learn more about probability here:
brainly.com/question/1210781
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