For each of the following paris of events, explain why A and B are dependent or

Question

For each of the following paris of events, explain why A and B are dependent or independent.

(a)Consider the population of U.S college freshman, from which a student is randomly selected. Let A denote the event that the student attends the College of William & Mary, let B denote the event that the student graduated from high school in Virginnia.

(b)Consider the population of all persons(living or dead) who have earned a Ph.D. drom an American university, from which one is randomly selected. Let A denote the event that the person's Ph.D was earned before 1950 and let B denote the event that the person is female.

Explanation / Answer

(a)Consider the population of U.S college freshman, from which a student is randomly selected. Let A denote the event that the student attends the College of William & Mary, let B denote the event that the student graduated from high school in Virginnia.

The events are independent because students attending the College of William & Mary need not have graduated from high school in Virginnia and vice versa is also true.

(b)Consider the population of all persons(living or dead) who have earned a Ph.D. drom an American university, from which one is randomly selected. Let A denote the event that the person's Ph.D was earned before 1950 and let B denote the event that the person is female.

These events are independent because the year of earning Ph.D is not dependent on gender or vice versa.

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