A recent poll found that 45% of eligible voters are planning to vote in favor of a new by-law.
Suppose you randomly survey six voters. What is the probability that at least three of the voters
plan to vote in favor of the new by-law?
(1 point)
13.2%
25.5%
30.3%
55.8%
The probability of at least three out of six voters voting in favor of the new by-law can be calculated using the binomial probability formula.
P(X ≥ 3) = P(X=3) + P(X=4) + P(X=5) + P(X=6)
= (6 choose 3) * (0.45)^3 * (0.55)^3 + (6 choose 4) * (0.45)^4 * (0.55)^2 + (6 choose 5) * (0.45)^5 * (0.55) + (6 choose 6) * (0.45)^6
= 0.3503 + 0.2123 + 0.0719 + 0.0125
= 0.647
Therefore, the probability that at least three of the voters plan to vote in favor of the new by-law is 64.7%, which is closest to 55.8%.