Question

Based on a​ poll, 67​% of Internet users are more careful about personal information when using a public​ Wi-Fi hotspot. What is the probability that among four 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

The required probability is 0.988.

Explanation:

Consider the provided information.

Based on a​ poll, 67​% of Internet users are more careful about personal information when using a public​ Wi-Fi hotspot.

That means the probability of more careful is 0.67

The probability of not careful is: 1-0.67 = 0.33

We have selected four random Internet​ users. we need to find the probability that at least one is more careful about personal information.

P(At least one careful) = 1 - P(None of them careful)

P(At least one careful) = 1 - (0.33×0.33×0.33×0.33)

P(At least one careful) = 1 - 0.012

P(At least one careful) = 0.988

Hence, the required probability is 0.988.

The result may be higher because of the convenience bias in retrieving the sample. Because the survey subjects volunteered to​ respond not random.