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A poll was conducted among 250 residents of a certain city regarding tougher gun-control laws. The results of the poll are shown in the table: $$ \begin{array}{lccccc} \hline & \begin{array}{c} \text { Own } \\ \text { Only a } \\ \text { Handgun } \end{array} & \begin{array}{c} \text { Own } \\ \text { Only a } \\ \text { Rifle } \end{array} & \begin{array}{c} \text { Own a } \\ \text { Handgun } \\ \text { and a Rifle } \end{array} & \begin{array}{c} \text { Own } \\ \text { Neither } \end{array} & \text { Total } \\ \hline \text { Favor } & & & & & \\ \text { Tougher Laws } & 0 & 12 & 0 & 138 & 150 \\ \hline \begin{array}{l} \text { Oppose } \\ \text { Tougher Laws } \end{array} & 58 & 5 & 25 & 0 & 88 \\ \hline \text { No } & & & & & \\ \text { Opinion } & 0 & 0 & 0 & 12 & 12 \\ \hline \text { Total } & 58 & 17 & 25 & 150 & 250 \\ \hline \end{array} $$ If one of the participants in this poll is selected at random, what is the probability that he or she a. Favors tougher gun-control laws? b. Owns a handgun? c. Owns a handgun but not a rifle? d. Favors tougher gun-control laws and does not own a handgun?

Step by step solution

01

Find the number of participants who satisfy each condition

Using the provided table, we can find the number of participants who satisfy each of the four conditions. a. Favors tougher gun-control laws: 150 people. b. Owns a handgun: 58 people who own only a handgun and 25 people who own both a handgun and a rifle, for a total of 58 + 25 = 83 people. c. Owns a handgun but not a rifle: 58 people. d. Favors tougher gun-control laws and does not own a handgun: 12 people who own only a rifle and 138 people who own neither, for a total of 12 + 138 = 150 people (note that in this case, the number is the same as the number who favor tougher laws, because there are 0 people who favor tougher laws and own a handgun).

02

Calculate the probabilities

Now that we have the number of participants who satisfy each condition, we can find the probability for each case by dividing the number of participants who satisfy the condition by the total number of participants (250). a. P(Favors tougher gun-control laws) = 150 / 250 = \(0.6\) b. P(Owns a handgun) = 83 / 250 = \(0.332\) c. P(Owns a handgun but not a rifle) = 58 / 250 = \(0.232\) d. P(Favors tougher gun-control laws and does not own a handgun) = 150 / 250 = \(0.6\) The answers to the four cases are: a. The probability that a randomly-selected participant favors tougher gun-control laws is \(0.6\). b. The probability that a randomly-selected participant owns a handgun is \(0.332\). c. The probability that a randomly-selected participant owns a handgun but not a rifle is \(0.232\). d. The probability that a randomly-selected participant favors tougher gun-control laws and does not own a handgun is \(0.6\).

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