Question

In: Statistics and Probability

At this college, 28% are students of color, 6% of students are veterans, and 1.32% are...

At this college, 28% are students of color, 6% of students are veterans, and 1.32% are both veterans and students of color.

(a) If a randomly selected student is a student of color, what is the probability that the student is a veteran?

(b) Is the event of being a student of color independent of the event of being a veteran? Explain your answer by using probability concepts.

Solutions

Expert Solution

28% are students of color

P[ students of color ] = 28% = 0.28

6% of students are veterans

P[ students are veterans ] = 6% = 0.06

1.32% are both veterans and students of color

P[ both veterans and students of color ] = 1.32% = 0.0132

(a) If a randomly selected student is a student of color, what is the probability that the student is a veteran?

P[ student is a veteran | student of color ] = P[ both veterans and students of color ] / P[ students of color ]

P[ student is a veteran | student of color ] = 0.0132 / 0.28

P[ student is a veteran | student of color ] = 0.047

(b) Is the event of being a student of color independent of the event of being a veteran? Explain your answer by using probability concepts.

If the two events are independent then

P[ student is a veteran | student of color ] = P[ students are veterans ] should hold

but here

P[ student is a veteran | student of color ] P[ students are veterans ]

Hence, the events are dependent

orchestra answered 1 year ago
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