Question

Suppose that 60% of the voters in a state intend to vote for a certain candidate. what is the probability that a survey polling 6 people reveals that at least two intend to vote for that candidate?

Answer 1

The probability that a survey polling 6 people reveals that at least two intend to vote for the candidate is approximately 0.8807.

Step-by-step explanation:

To find the probability that at least two out of six people will intend to vote for the candidate, we need to calculate the probability of the different possible outcomes. Let's consider three cases:

1. No one intends to vote for the candidate: The probability of this case is (0.4)⁶ = 0.004096.
2. Exactly one person intends to vote for the candidate: The probability of this case is 6*(0.4)⁵*(0.6) = 0.1152.
3. Two or more people intend to vote for the candidate: The probability of this case is 1 - (probability of case 1 + probability of case 2) = 1 - (0.004096 + 0.1152) = 0.8807.

Therefore, the probability that a survey polling 6 people reveals that at least two intend to vote for the candidate is approximately 0.8807.

Answer 2

This is a very complete survey at all. I wouldn't trust it. I'm guessing maybe about a 50% chance that this poll would duplicate the more complete poll. I would think that you would have to poll at least 1000 people for a poll like this to be trustworthy. I would sure hope that polls are not taken this way. There are so many polls taken out there now a days. I think besides the number of people surveyed, the other thing that makes a huge difference is how the questions are asked. Many polling questions are very loaded with leading questions.