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A survey involving 800 likely Democratic voters and 500 likely Republican voters asked the question: Do you support or oppose legislation that would require trigger locks on guns, to prevent misuse by children? The following results were obtained: Answer Democrats,% Republicans,% Support 88 74 Oppose 7 16 Don't know/refused 5 10 If a randomly chosen respondent in the survey answered "support," what is the probability that he or she is a likely Republican voter? (Round your answer to three decimal places.)

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Answer-

The probability that the person is a Republican given that they answered support is 0.3445 or 34.45%

Solution-

In the survey,

Number of Democratic voters = 800

Number of Republican voters = 500

Total voters = 800 + 500 = 1300

*Refer the table attached below

Multiplying the percentages to the total number the table was obtained.

We have to calculate the the probability that the person is a Republican given that they answered "support".

So,

[tex]\text{P(Republican}\ |\ \text{Support})=\dfrac{\text{P(Republican}\ \cup \ \text{Support)}}{\text{P(Support)}}[/tex]

From the table,

[tex]\text{P(Republican)}=\dfrac{500}{1300},\\\\\text{P(support)}=\dfrac{1074}{1300},\\\\\text{P(Republican}\ \cup \ \text{support)}=\dfrac{370}{1300}[/tex]

Putting the values,

[tex]\text{P(Republican}\ |\ \text{Support})=\dfrac{\frac{370}{1300}}{\frac{1074}{1300}} =\dfrac{370}{1074}=0.3445=34.45\%[/tex]

Therefore, the probability that the person is a Republican given that they answered support is 0.3445 or 34.45%

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