Probability And Statistics Applications

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Probability and Statistics Applications1)In a particular suburb, 30% of the households have installed electronic securitysystems.a)If a household is chosen at random from this suburb, what is the probabilitythat this household has not installed anelectronic security system?b)If two households are chosen at random from this suburb, what is theprobability that neither has installed an electronic security system?Answer:a)If 30% of households have installed an electronic security system,then the probability that a randomly chosen householdhas notinstalled anelectronic security system is:P(Nosecuritysystem)=1−P(Hassecuritysystem)=1−0.30=0.70P(\text{No securitysystem}) = 1-P(\text{Has security system}) = 1-0.30 = 0.70So, the probability that the household has not installed an electronic security systemis0.70.b)If two households are chosen at random, and both are independent of each other,the probability thatneitherhousehold has installed an electronic security system is:P(Neitherhassecuritysystem)=P(Nosecuritysystemfor1sthousehold)×P(Nosecuritysystemfor2ndhousehold)P(\text{Neither has security system}) = P(\text{Nosecurity system for 1st household})\times P(\text{No security system for 2ndhousehold}) =0.70×0.70=0.49= 0.70\times 0.70 = 0.49So, the probability that neither household has installed an electronic security systemis0.49.5)In a study designed to gauge married women’s participation in the workplacetoday, the data provided in the fileP04_05.xlsxwere obtained from a sample of 750randomly selected married women. Consider a woman selected at random from thissample in answering the following questions.a)What is the probability that this randomly selected woman has a job outsidethe home?b)What is the probability that this randomly selected woman has at least onechild?c)What is the probability that this randomly selected woman has a full-time joband no more than one child?d)What is the probability that this randomly selected woman has a part-time jobor at least one child, but not both?

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