In a large population, 3% have had a heart attack. Suppose a medical researcher randomly selects two people. Let X represent the event the first person has had a heart attack. Let Y represent the event the second person has had a heart attack. Which of the following is true about the two events?
(A) X and Y are disjoint.
(A) X and Y are independent.
(C) None of the above are true.
(D) Both (A) and (B) are true.
Explain your answer..
In probability two or more events are said to be disjoint when there is no intersection of any of these events. An intersection of two events means that they happen at the same time. They can also be called mutually exclusive.
Answer and Explanation:
First of all, these 2 events can happen at the same time where both the first and the second person have had a heart attack. Therefore, they are NOT disjoint. They are independent since the probability of X doesn't change the probability of Y, and vice versa, assuming that we have a large enough population. Finally, the answer is B.
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from High School Algebra II: Help and ReviewChapter 25 / Lesson 8