Question

Thirty percent of the students at a local high school face a disciplinary action of some kind before they graduate. Of those "felony" students, 40% go on to college. Of the ones who do not face disciplinary action 60% go on to college. Show if events faced disciplinary action and went to college are independent or not.

Answer 1

Answer:

Not independent

Step-by-step explanation:

For two events to be independent, they must not effect each other. For two independent events, changes in one of the event do not cause any change on the other event.

To explain it in terms of probability, let's first define and calculate the probabilities:

P(F) : Probability of facing felony

P(C) : Probability of going to college

P(F ∩ C) : Probability of facing felony and going to college

P(F° ∩ C): Probability of not facing a felony and going to college

Assume we have 100 students:

Faced felony = 0.3 * 100 = 30

Faced felony and go college = 30 * 0.4 = 12

Not faced felony = 0.7 * 100 = 70

Not faced felony and go college = 0.6 * 70 = 42

Total of going to college = 12 + 42 = 54

So P(C) = 54 / 100 = 0.54

If P(F)*P(C) = P(F ∩ C), then these two events are independent. If not, they are not independent.

Let's calculate the probabilities:

As given in the question, 30% of students face felony so P(F) = 0.3

P(C) = P(C ∩ F) + P(C ∩ F°) = 0.12 + 0.42 = 0.54

P(F) = 0.3

P(F ∩ C) = 0.12

P(F)*P(C) = 0.3 * 0.54 = 0.162 which ic not equal to P(F ∩ C). Therefore, these events are not independent.