Based on the data in two-way frequency table, "being in high school" and "gpa above 3.0" are not independent events.
The conditional probability is the happening of an event, when the probability of occurring of other event is given.
A two-way frequency table shows grades for students in college and students in high school.
Let H represent being in high school and G represent the GPA above 3.0. To be an independent event, they must be,
[tex]P(H|G)=P(H)[/tex]
The conditional probability of event H, given that the G is occurred, can be calculated as,
[tex]P(H|G)=\dfrac{14}{40}\\P(H|G)=0.35[/tex]
Total students below 3.0 GPA are 60 and the total number of student are 100. Thus, the probability of being in high school is
[tex]P(H)=\dfrac{60}{100}\\P(H)=0.6[/tex]
Here, conditional probability [tex]P(H|G)[/tex] is not equal to the probability of being in high school.
Hence, based on the data in two-way frequency table, "being in high school" and "gpa above 3.0" are not independent events.
Learn more about the probability here;
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