2022-02-25

A poll is give , showing 40% are in favor of a new building project.If 6 people are chosen at random, what is the probability that exactly 3 of them favor the new building project?

alenahelenash

Step 1
We will use binomial probability to solve this question.
The formula for the binomial probability is:
$P\left(x\right){=}^{n}{C}_{x}\cdot {p}^{x}\cdot {\left(1-p\right)}^{x}$, where
$n=$ sample size
$p=$ probability of success.
Given:
$n=6$,
$p=40\mathrm{%}=0.40$
$x=3$
Step 2 We need to find $P\left(x=3\right)$. The calculations are shown as follows:
$P\left(x=3\right){=}^{6}{C}_{3}\cdot {0.40}^{6}\cdot {\left(1-0.40\right)}^{6-3}$
$=0.0177$
Therefore, the probability that exactly $3$ of them favor the new building project is $=0.0177$.

Do you have a similar question?