The probability that out of 20, 14 agree to answer is:
P(14) = 0.109
We know that the 80% of the respondents will agree to answer the opinion poll (and 20% don't).
Then the probability that a random respondent agrees to answer the poll is 0.8
Now, the probability that out of 20, 14 agree to answer, is:
[tex]P(14) = C(20, 14)*(0.8)^{14}*(0.2)^6[/tex]
Where C(20, 14) is the number of different combinations of 14 elements that we can make out of the 20 elements (the number of permutations).
[tex]C(20, 14) = \frac{20!}{(20 - 14)!*14!} = \frac{20*19*18*17*16*15}{6*5*4*3*2} = 38,760[/tex]
Replacing that in the probability, we get:
[tex]P(14) = 38,760*(0.8)^{14}*(0.2)^6 = 0.109[/tex]
If you want to learn more about probability, you can read:
https://brainly.com/question/251701
