Question

A poll found that 68.3​% of citizens felt the government was not working well. If seven people were randomly​ selected, what is the probability that all seven felt the government is not working​ well?

Answer 1

Answer: 0.0693

Explanation:

Given : The probability of citizens felt the government was not working well = 0.683

The binomial distribution formula :-

$^nC_x\ p^x\ (1-p)^{n-x}$, where n is the number of trials and p is the probability of successes.

If seven people were randomly​ selected, then the probability that all seven felt the government is not working​ well is given by  :-

$P(x=7)=^7C_7\ (0.683)^7\ (1-0.683)^{7-7}\\\\=(1) (0.683)^7\(1)=0.0693337876116\approx0.0693$

Thus , the required probability : 0.0693