Given:
A poll is given, showing 80% are in favor of a new building project.
That is, the probability of success is p=0.8
Sample size, n=6
The number of times for a specific outcome within n trials is x=2.
To find the probability that exactly 2 of them favor the new building project:
Using the binomial probability,
[tex]P\mleft(x\mright)=^nC_x\cdot p^x\cdot\mleft(1-p\mright)^{n-x}[/tex]Substituting the given values, we get,
[tex]\begin{gathered} P(2)=^6C_2(0.8)^2(1-0.8)^{6-2} \\ =\frac{6!}{(6-2)!2!}(0.64)(0.2)^4 \\ =15\times0.64\times0.0016 \\ =0.01536 \end{gathered}[/tex]Thus, the probability that exactly 2 of them favor the new building project is 0.01536.
