2. Sample spaces and events At 100 college campuses, 1,200 full-time undergradua
ID: 3075333 • Letter: 2
Question
2. Sample spaces and events At 100 college campuses, 1,200 full-time undergraduate students were surveyed on their credit card usage. Among seniors, 57% reported that they didn't have a credit card in their own name, and 18% reported that they had at least one credit card in their own name and they maintained a credit card balance. [Source: Glater, J.D. (2008, December 31). The debt trap: Colleges profit as banks market credit cards to students. The New York Times.] Consider this random experiment. A college senior is randomly selected. The senior is interviewed and then categorized into one of the following three categories: she does not have a credit card in her own name, she has at least one credit card in her own name and pays her credit card balance in full each month, or she has at least one credit card in her own name and maintains a credit card balance. Consider the following events. O The senior does not have a credit card in her own name. C -The senior has at least one credit card in her own name. F - The senior has at least one credit card in her own name and pays her credit card balance in fll each month. The senior has at least one credit card in her own name and maintains a credit card balance. The events B and F are not mutually exclusive. Event oExplanation / Answer
Events B and F are mutually exhaustive events.
Mutually exhaustive events are the events that cannot happen simultaneously at the same time. Events B and F, too, cannot happen simultaneously, as, the senior may either maintain credit card balance or can pay it off in full each month. a senior cannot be doing both.
Events O, B, F are exhaustive events.
in the experiment, if any senior is selected at random, then he or she will definately be from either O, B or F. there are no more categories in which a senior selected at random could belong.
Event O is a simple event.
A simple event is the event which has just a single outcome. there is only one outcome in the event O.
The set S=<O,F> is not the correct description of the sample space for the random experiment because the events in S are not Mutually exhaustive events for this particular experiment. As in, the complete sample space will have all the categories of the seniors stated in the question. event S misses out on the seniors that have at least one credit card in their name and maintain a credit card balance.
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