Final answer:
To find the probability that a randomly selected voter supports neither Measure R nor Measure S, we subtract the total percentage of voters that support either measure (66%) from 100%, resulting in 34%.
Step-by-step explanation:
To find the probability that a randomly selected voter supports neither Measure R nor Measure S, we can use the principle of inclusion-exclusion. According to the given poll percentages, 58% support Measure R, 47% support Measure S, and 39% support both. The principle of inclusion-exclusion tells us to add the probabilities of each group separately and then subtract the intersection once (since we've counted it twice).
The calculation would be as follows:
- P(R) = 58%
- P(S) = 47%
- P(R and S) = 39%
- P(R or S) = P(R) + P(S) - P(R and S)
- P(R or S) = 58% + 47% - 39% = 66%
The probability that a voter supports either measure is 66%. To find the probability of a voter supporting neither, we subtract from 100%:
- P(neither R nor S) = 100% - P(R or S)
- P(neither R nor S) = 100% - 66% = 34%
Therefore, the probability that a randomly selected voter supports neither measure is 34%.