Question

based on a poll, 70% 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? the probability that at least one of them is careful about personal information is . (round to three decimal places as needed.) how is the result affected by the additional information that the survey subjects volunteered to respond? a. the result should not be impacted by this because volunteers are likely to have the most relevant responses. b. it is very possible that the result is not valid because the sample may not be representative of the people who use public wi - fi. c. the result should not be impacted by this because there is no reason to lie when responding. d. it is very possible that the result is not valid because not everyone uses public wi - fi.

Explanation:

Step1: Find the probability of none being careful

The probability that an internet - user is not careful is $1 - 0.7=0.3$. For 4 independent users, the probability that none of them is careful is $(0.3)^4$ according to the multiplication rule for independent events.
$(0.3)^4 = 0.0081$

Step2: Find the probability of at least one being careful

The probability of at least one being careful is the complement of the probability of none being careful. Let $P(X\geq1)$ be the probability of at least one being careful and $P(X = 0)$ be the probability of none being careful. Then $P(X\geq1)=1 - P(X = 0)$.
$P(X\geq1)=1-(0.3)^4=1 - 0.0081 = 0.9919\approx0.992$

For the multiple - choice part:
When the survey subjects volunteered to respond, it is very possible that the sample may not be representative of the people who use public Wi - Fi. This is a form of non - response bias. Volunteers may have different characteristics or concerns compared to non - volunteers.

Answer:

The probability that at least one of them is careful about personal information is $0.992$.
B. It is very possible that the result is not valid because the sample may not be representative of the people who use public Wi - Fi.