School administrators asked a group of students and teachers which of two school logo ideas, logo A or logo B, they prefer. This table shows the results.
Logo A
Logo B
Total
Students
14
86
100
Teachers
14
11
25
Total
28
97
125
Are being a student and preferring logo B independent events? Why or why
not?

The events are not independent

Step-by-step explanation:

Given

Logo A --- Logo B ---Total

Students 6733100

Teachers 11 14  25

Total 7847125

Required

Determine if being a student and preferring logo A are independent events

Let P(S) represent probability of being a student

Let P(Logo A) represent probability of preferring logo A

Let P(S n Logo A) represent probability of  being a student and preferring logo A

To determine if they are independent, we have to calculate

P(S), P(Logo A) and P(S n Logo A)

P(S) = Total Students / Total Population

P(Logo A) = Total that prefers Logo A / Total Population

P(S n Logo A) = Number of students that prefer logo A /  Total Population

If the events are independent, then the following condition must be satisfied

Substitute the values of P(S), P(Logo A) and P(S n Logo A)

Since they are not equal, then the events are not independent

Step-by-step explanation:

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