Let A be the event that a student is enrolled in an accounting course, and let S be the event that a student is enrolled in a statistics course. It is known that 30% of all students are enrolled in an accounting course and 40% of all students are enrolled in statistics. Included in these numbers are 15% who are enrolled in both statistics and accounting.Given the prior knowledge that a student is enrolled in accounting, what is the probability that this student is also enrolled in statistics?Question 32Select one:a.0.75b.0.15c.0.50d.0.375
Question
Let A be the event that a student is enrolled in an accounting course, and let S be the event that a student is enrolled in a statistics course. It is known that 30% of all students are enrolled in an accounting course and 40% of all students are enrolled in statistics. Included in these numbers are 15% who are enrolled in both statistics and accounting.Given the prior knowledge that a student is enrolled in accounting, what is the probability that this student is also enrolled in statistics?Question 32Select one:a.0.75b.0.15c.0.50d.0.375
Solution
The question is asking for the conditional probability that a student is enrolled in statistics given that they are enrolled in accounting. This is represented as P(S|A).
We know that P(S and A), the probability of a student being enrolled in both statistics and accounting, is 15% or 0.15.
We also know that P(A), the probability of a student being enrolled in accounting, is 30% or 0.30.
The formula for conditional probability is P(S|A) = P(S and A) / P(A).
Substituting the given values into the formula gives us P(S|A) = 0.15 / 0.30 = 0.50.
So, the probability that a student is enrolled in statistics given that they are enrolled in accounting is 0.50.
Therefore, the correct answer is c. 0.50.
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