15. The sample space that describes the two-way classification of citizens accor

Question

15. The sample space that describes the two-way classification of citizens according to gender and opinion on a political issue is S (mf,ma,mn,ff,fa,fn), where the first letter denotes gender (m: male,f female) and the second opinion (F for, a: against, n: neutral). For each of the following events in the experiment of selecting a citizen at random, state the complement of the event in the simplest possible terms, then find the outcomes that comprise the event and its complement. The person is male. a. b. The person is not in favor. C. The person is either male or in favor. d· The person is female and neutral.

Explanation / Answer

a) complement of evnt is person is female.

oucome in event person is male ={ mf ; ma ; mn}

oucome in complement event person is female ={ ff ; fa ; fn}

b)  complement of event is person is in favour

oucome in event person is not in favour={ ma ; mn ; fa ; fn}

oucome in complement event person is in favour={ mf ;ff }

c)complement of event is person is female and not in favour.

oucome in event person is either male or in favour ={mf ; ma ; mn ; ff}

oucome in complement event person is female and not in favour ={ fa ; fn}

d) complement of event is male or not neutral ={mf ; ma ; mn ; ff ; fa}

oucome in event person person is female and neutral ={fn}

outcome in complement of event is male or not neutral ={mf ; ma ; mn ; ff ; fa}

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