In 2002, approximately 39% of the people eligible to vote in mid-term elections voted. Suppose you have taken a sample of 7 eligible voters. What is the probability of having sampled exactly 0 people that voted?

Answer 1

The probability of having sampled exactly 0 people that voted is calculated using the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

Where:
- n is the number of trials (sample size)
- k is the number of successful outcomes (0 people voted in this case)
- p is the probability of a successful outcome (percentage of people who voted)

In this case, n = 7, k = 0, and p = 0.39.

P(X = 0) = (7 choose 0) * 0.39^0 * (1-0.39)^(7-0)
= 1 * 1 * 0.61^7
= 0.61^7
= 0.04131

Therefore, the probability of having sampled exactly 0 people that voted is approximately 0.04131 or 4.131%.