Question

n a​ poll, 6767​% of Internet users are more careful about personal information when using a public​ Wi-Fi hotspot. What is the probability that among threethree randomly selected Internet​ users, at least one is more careful about personal information when using a public​ Wi-Fi hotspot? How is the result affected by the additional information that the survey subjects volunteered to​ respond?

Answer 1

Answer:

The probability that among three randomly selected Internet​ users, at least one is more careful about personal information when using a public​ Wi-Fi hotspot is 0.964

If the survey subjects volunteered to​ respond , then those with the strongest opinions are most likely respond. The survey sample is then not randomly selected, the survey may have a response bias.

Explanation:

Let P(at least one is more careful about personal information when using a public​ Wi-Fi hotspot) denote the probability that among three randomly selected Internet​ users, at least one is more careful about personal information when using a public​ Wi-Fi hotspot, then we have the equation

P(at least one is more careful about personal information when using a public​ Wi-Fi hotspot) = 1 - P(none of the selected users is more careful about personal information when using a public​ Wi-Fi hotspot)

• If 67​% of Internet users are more careful about personal information when using a public​ Wi-Fi, then 33% of them are not.

P(none of the selected users is more careful about personal information when using a public​ Wi-Fi hotspot) = $0.33^{3}$ ≈ 0.036

P(at least one is more careful about personal information when using a public​ Wi-Fi hotspot)  = 1 - 0.036 = 0.964