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The total voters identify as independent is$46\%$and independents voted in the election$35\%$.

The voters identify as liberals$30\%$and liberals voted in the election $62\%$.

The voters identify as conservatives$24\%$and conservatives voted in the election$58\%$.

A voter is chosen at random

$\text{Probability of an event}=\frac{\text{Number of favorable outcomes}}{\text{Number of total outcomes}}$

Assume, the total number of people be x.

Number of people who identify as independent =0.46x

Total number of voters$=(0.46×0.35x)+(0.3×0.62x)+(0.24×0.58x)=0.4862x$

Number of independent voters $=0.35×0.46x=0.161x$

Probability that a voter selected at random is an independent voter$=\frac{0.161x}{0.4862x}=\frac{805}{2431}=0.3311$

Number of people who identify as liberal$=0.30x$

Number of liberal voters$=0.62×0.30x=0.186x$

Probability that a voter selected at random is a liberal voter$=\frac{0.186x}{0.4862x}=\frac{930}{2431}=0.3825$

Number of people who identify as conservative$=0.24x$

Number of conservative voters$=0.58×0.24x=0.1392x$

Probability that a voter selected at random is a conservative voter$=\frac{0.1392x}{0.4862x}=\frac{696}{2431}=0.2863$

Total number of voters who participated in the election$=0.2432x$

Percentage of voters who participated in the election$=\frac{0.2432x}{x}×100=24.32\%$