In a recent survey of computer ownership, 73% of the repondents indicated they o

Question

In a recent survey of computer ownership, 73% of the repondents indicated they own PC computers,while 21.8% indicatedthey own both PC and Mac computers, and 80.1% said the own at least one of the two computers.
a. What is the probability that a respondent owns a Mac computer?
b. Given that a respondent owns a PC, what is the probability that the repsondent also owns a Mac?
c. Are events "P" and "M" mutually exclusive? Why or why not? Explain using probabilities.
d. Are the two events "P" and "M" independent? Explain using probabilities.

Explanation / Answer

In a recent survey of computer ownership, 73% of the repondents indicated they own PC computers,while 21.8% indicatedthey own both PC and Mac computers, and 80.1% said the own at least one of the two computers. here, If 80.1% of respondents has at least one of the two computer and 73% has PC computer that means (80.1-73)%= 7.1% has only mac computers but not pc. Furthermore, if 21.8% owe both computer then total percent of respondents who has mac computers = (7.1+21.8)% =28.9% and percent of owner who owe only pc but not mac= (73-21.8)%=51.2% a. What is the probability that a respondent owns a Mac computer? Probability of respondents owning a mac = (percent of mac owner/total percent) = 28.9/100 = 0.289 b. Given that a respondent owns a PC, what is the probability that the repsondent also owns a Mac? Probability of respondents who owe pc also owning mac= (percent of both owners/ percent of pc owners) = 21.8/73 = 0.299 (approx.) c. Are events "P" and "M" mutually exclusive? Why or why not? Explain using probabilities. “P” and “M” are mutually exclusive if and only if occurrence of “P” means not occurring of “M” and vice versa, but that is not the case here. If a respondent owes a PC that cannot refer whether or not the respondent owes mac. Thus, they are not mutually exclusive. To prove two events are mutually exclusive prove P(P or M) = P(P) + P(M) else they are dependent. d. Are the two events "P" and "M" independent? Explain using probabilities. "P" and "M" are independent if occurrence of one does not affect occurrence of other. To prove two events are independent prove P(P and M) = P(P).P(M) else they are dependent.

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