1. ## Probability help

A survey involving 600 likely Democratic voters and 200 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 results are displayed in the table below. 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.)

support 85% republicans 72% Dem
oppose 8% 17%
Dont Know/refused 7% 11%

A survey involving 600 likely Democratic voters and 200 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 results are displayed in the table below. 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.)

support 85% republicans 72% Dem
oppose 8% 17%
Dont Know/refused 7% 11%
Draw a tree diagram (the first two branches are R and D). It should then be clear that

$\displaystyle \Pr( R \, | \, \text{support} ) = \frac{(0.75)(0.85)}{(0.75)(0.85) + (0.25)(0.72)} = ....$