Question

Who will you vote for? In a survey of 500 likely voters in a certain city, 255 said that they planned to vote to reelect the incumbent mayor.
What is the probability that a surveyed voter plans to vote to reelect the mayor? Express your answer as a decimal rounded to two decimal places.

Answer 1

To find the probability that a surveyed voter plans to vote to reelect the mayor, we can use the formula for probability:

\[
P(\text{reelect}) = \frac{\text{number of voters who plan to reelect}}{\text{total number of voters surveyed}}
\]

In this case, the number of voters who plan to reelect the incumbent mayor is 255, and the total number of voters surveyed is 500.

Substituting the numbers into the formula gives us:

\[
P(\text{reelect}) = \frac{255}{500}
\]

Now, we can calculate this:

\[
P(\text{reelect}) = 0.51
\]

Thus, the probability that a surveyed voter plans to vote to reelect the mayor is:

\[
\boxed{0.51}
\]

Answer 2

(b) Interpret this probability by estimating the percentage of all voters in the city who plan to vote to reelect the mayor.

Answer 3

The probability \( P(\text{reelect}) = 0.51 \) indicates that approximately 51% of the surveyed voters plan to vote to reelect the incumbent mayor.

To interpret this probability as a percentage, we can multiply by 100:

\[
\text{Percentage} = P(\text{reelect}) \times 100 = 0.51 \times 100 = 51\%
\]

Therefore, based on the survey, we can estimate that about **51%** of all voters in the city plan to vote to reelect the mayor.