1-Complements – What is wrong with the expression P(A) + P() = 0.0? 2-Disjoint E
ID: 3216640 • Letter: 1
Question
1-Complements – What is wrong with the expression P(A) + P() = 0.0?
2-Disjoint Events – For a Gallop poll, F is the event of randomly selecting a female, and D is the event of randomly selecting a Democrat. Are events F and D disjoint? Why or why not?
For Exercises 3-5, determine whether the two events are disjoint for a single trial.
3-Arriving late for your next doctor’s appointment.
Arriving early for your next doctor’s appointment.
4-Randomly selecting a statistics student and getting one who uses the textbook in class.
Randomly selecting a statistics student and getting one who does not own the textbook.
5-Randomly selecting someone who travels from Carbondale to Chicago by train.
Randomly selecting someone who travels from Carbondale to Chicago by automobile
Explanation / Answer
1) The given statement is False because the sum of probabilities of an event and its complement is always 1 not 0.
2) The 2 events here are not disjoint because disjoint events are the ones which cannot happen together at any cost that is P(A and B) = 0 but here as we can have female democrats, therefore the intersection of these 2 events is not 0 here.
3) Arriving late for doctor's appointment means that doctor cannot arrive early for it. Therefore the 2 events given here cannot happen together and hence the 2 events are disjoint.
4) Randomly selecting a student who uses textbook and randomly selecting a student and getting who does not own a textbook are disjoint events as they cannot happen together unless a student who does no owns a tectbook uses someone else textbook.
5) The 2 events here are disjoint unless there is someone who travels by both train and automobile. There must be some people travelling by both train and automobile. Thus the 2 events may or may not be disjoint depending on the conditions explained. We should just keep in mind that the disjoint events are the ones which cannot happen together.
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