Question

A poll shows that 30% of voters in a city favor of a $0.01 tax increase. If 8 voters are selected at random, what is the probability that exactly 2 of them will vote in favor of the tax?

Answer 1

Answer: 0.2965

Explanation:

Given : The proportion of voters in a city favor of a $0.01 tax increase. =0.30

The number of voters are selected at random =8

Binomial probability formula :-

$P(X)=^nC_x \ p^x\ (1-p)^{n-x}$, where P(x) is the probability of getting success in x trials, n is total number of trials and p is the probability of getting success in each trial.

Now, the probability that exactly 2 of them will vote in favor of the tax is given by :-

$P(2)=^8C_2 \ (0.30)^3\ (0.70)^{8-6}\\\\=\dfrac{8!}{2!6!}(0.30)^2\ (0.70)^{8-2}\\\\=0.29647548\approx0.2965$

Hence,  the probability that exactly 2 of them will vote in favor of the tax = 0.2965