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.From the above information it can be concluded that _______.Question 14Select one:a.A and S are independentb.A and S are mutually exclusivec.A and S are not independentd.A and S are complements
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.From the above information it can be concluded that _______.Question 14Select one:a.A and S are independentb.A and S are mutually exclusivec.A and S are not independentd.A and S are complements
Solution
The answer is c. A and S are not independent.
Here's why:
Two events A and B are said to be independent if the occurrence of A does not affect the occurrence of B, and vice versa. In other words, Events A and B are independent if P(A ∩ B) = P(A)P(B).
In this case,
P(A) = Probability of a student enrolled in an accounting course = 0.30 P(S) = Probability of a student enrolled in a statistics course = 0.40 P(A ∩ S) = Probability of a student enrolled in both courses = 0.15
If A and S were independent, then P(A ∩ S) should be equal to P(A)P(S) = 0.30 * 0.40 = 0.12. But, P(A ∩ S) is given as 0.15, which is not equal to 0.12.
Therefore, A and S are not independent.
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