<p>A university requires its biology majors to take a course called BioResearch. The prerequisite for this course is that students must have taken either a statistics course or a computer course. By the time they are juniors, 52% of the Biology majors have taken Statistics, 23% have had a computer course, and 7% have done both.
a.) What percent of the junior Biology majors are ineligible for BioResearch?
b.) what is the probability that a junior Biology major who has taken Statistics has also taken a computer course?
c.) are taking these two courses disjoint events? Explain
d.) Are taking these two course independent? Explain</p>
<p>This isn’t even a SAT math question bro.</p>
<p>a) 1 - [ (.52 - .7) + (.23 - .7) ] </p>
<p>b) 7% because 7% have taken both so that’s 7% of the population of biology majors who have</p>
<p>c) They’re not because if they were, the probability that a student could take both is 0%. </p>
<p>d) Yeah, because they’re two different courses and from the information given, you can’t tell if there’s any time schedule or anything.</p>
<p>^^
(1) Subtracting the 7% from both is incorrect. This is easy to see by drawing a large circle to represents all bio majors, a mid-size circle (inside the big-circle) that takes up 52% of the area of the big circle to represent those bio majors who take stat, and a small-circle (inside the big-circle) that overlaps the mid-size circle to represent those bio majors who take computer science. The area of overlap of the mid-size circle and the small-circle is 7% of the total area of the large circle.</p>
<p>Now add the none overlap areas of the mid-size and small circle, and to that add the overlap:
You get (in percent) 52 + 23 - 7 = 68 %. That’s .68.</p>
<p>(2) Consider only the students who have taken statistics. That’s the mid-size circle in (1). And for these students what fraction have taken computer science? The fraction is 7/52 (and not 7% since we have limited the question to a specific group of students).</p>