Question

A poll is given, showing 20% are in favor of a new building project.If 7 people are chosen at random, what is the probability that exactly 6 of them favor the new building project?

Answer 1

Recall the binomial probability

`\begin{gathered} P(x)=\binom{n}{x}\cdot p^x\cdot(1-p)^(n-x) \\ \text{where} \\ n\text{ is the sample size} \\ p\text{ is the probability of success} \end{gathered}`

We have the following given

n = 7

p = 20% → 0.2

x = 6

Substitute these values and solve for the probability

`\begin{gathered} P(x)=\binom{n}{x}\cdot p^x\cdot(1-p)^(n-x) \\ P(6)=\binom{7}{6}\cdot(0.2)^6\cdot(1-0.2)^(7-6) \\ P(6)=\binom{7}{6}\cdot(0.2)^6\cdot(0.8)^1 \\ P(6)=0.0003584 \end{gathered}`

Therefore, the probability is 0.0003584.