Question

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.)

Answer 1

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,

`\text{P(Republican}\ |\ \text{Support})=\frac{\text{P(Republican}\ \cup \ \text{Support)}}{\text{P(Support)}}`

From the table,

`\text{P(Republican)}=(500)/(1300),\\\\\text{P(support)}=(1074)/(1300),\\\\\text{P(Republican}\ \cup \ \text{support)}=(370)/(1300)`

Putting the values,

`\text{P(Republican}\ |\ \text{Support})=((370)/(1300))/((1074)/(1300)) =(370)/(1074)=0.3445=34.45\%`

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