Question

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?

13.2%
25.5%
30.3%
55.8%

Answer 1

i think its D

Answer 2

The solution is found by using the binomial distribution to find P(4 in favor), P(5 in favor) and P(6 in favor). These three values of probability are then added to find the required probability.
Do you want me to help with the probability calculations?

Answer 3

im confused on how to get it started

Answer 4

i was right! nvm .:)

Answer 5

If there are n trials with p probability of success on each trial, then the probability of exactly x successes is
\[P(X=x)=\left(\begin{matrix}n \\ x\end{matrix}\right)p ^{x}(1-p)^{n-x}\]
where
\[\left(\begin{matrix}n \\ x\end{matrix}\right)=nCx\]
The calculation for P(4 in favor) is
\[P(4)=\left(\begin{matrix}6 \\ 4\end{matrix}\right)0.45^{4}\times 0.55^{2}=0.18606\]
Now you need to calculate P(5) and P(6).

Answer 6

Actually you need to calculate P(3) + P(4) + P(5) + P(6)

Answer 7

Another method is to calculate P(0) + P(1) + P(2) and subtract the total from 1.