Suppose that 25% of all voters prefer Candidate A. If 6 people are chosen at random for a poll, what is the probability that exactly 2 of them favor Candidate A?

Answer 1

This question is best answered by referring to the binomial distribution as it follows all of the condition of a such a distribution:

1. The probability (25%) is constant and every outcome is equally likely (we don't have to worry about picking without replacement changing the probability of picking the next card as sample size (6) is much less than the population size (assumed to be much greater).
2. Each outcome is independent of each other.
3. The number of outcomes is finite.

The binomial distribution follows the probability mass function of: ₆C₂ * (0.25)² * (0.75)⁴

The binomial coefficient is 6!/(2! * 4!) = 15

The answer is thus: 29.7%