At 100 college campuses, 1,200 full-time undergraduate students were surveyed on

Question

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 25% reported that they had at least one credit card in their own name and they paid their credit card balance in full each month. [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 full each month. B The senior has at least one credit card in her own name and maintains a credit card balance. The events O and mutually exclusive. The events O and O exhaustive Event F a simple event. The set S = {O, F, B} the correct description of the sample space for the random experiment because the events in S are Find P(B) and P(C), and enter the probabilities in the following cells:

Explanation / Answer

Solution:-

Event O and C are mutually exclusive.

Because in probability theory, two events are mutually exclusive or disjoint if they cannot both be true (occur). A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both

The events O and C are exhaustive.

Because in probability theory and logic, a set of events is jointly or collectively exhaustive if at least one of the events must occur.

Event F is a simple event.

Simple events are the events where one experiment happens at a time and it will be having a single outcome.

The set S = {O,F,B} is the correct description of the sample space for the random experiment because the events in S are Exhaustive.

P(O) = 0.57, P(C) = 0.43

P(F) = 0.25, P(B) = 0.18

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