Question

For two programs at a university, the type

of student for two majors is as follows.

Find the probability a student is a science major,
given they are a graduate student.

Answer 1

0.72

Explanation:

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Answer 2

Explanation:

To find the probability that a student is a science major given that they are a graduate student, we need to use Bayes' theorem:

P(Science | Graduate) = P(Graduate | Science) * P(Science) / P(Graduate)

We know that P(Science) = 0.45 and P(Liberal Arts) = 0.55, and that P(Graduate | Science) = 0.35 and P(Graduate | Liberal Arts) = 0.25. We also know that the total probability of being a graduate student is:

P(Graduate) = P(Graduate | Science) * P(Science) + P(Graduate | Liberal Arts) * P(Liberal Arts)

Plugging in the values, we get:

P(Graduate) = 0.35 * 0.45 + 0.25 * 0.55 = 0.305

Now we can calculate the probability of being a science major given that the student is a graduate student:

P(Science | Graduate) = 0.35 * 0.45 / 0.305 = 0.515

Therefore, the probability that a student is a science major, given they are a graduate student, is approximately 0.515.