Question

based on a poll, 61% of internet users are more careful about personal information when using a public wi - fi hotspot. what is 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? 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.941 (round to three decimal places as needed.) how is the result affected by the additional information that the survey subjects volunteered to respond? a. it is very possible that the result is not valid because not everyone uses public wi - fi. b. the result should not be impacted by this because volunteers are likely to have the most relevant responses. c. 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. d. the result should not be impacted by this because there is no reason to lie when responding.

Explanation:

Step1: Find probability of none being careful

The probability that an Internet - user is not careful about personal information is $1 - 0.61=0.39$. Since the selections are independent, the probability that none of the three randomly selected users is careful is $P(\text{none})=(0.39)\times(0.39)\times(0.39)=0.39^{3}=0.059319$.

Step2: Find 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. So $P(\text{at least one}) = 1 - P(\text{none})=1 - 0.059319 = 0.940681\approx0.941$.
For the multiple - choice part:
When survey subjects volunteer to respond, there is a possibility of non - response bias. Volunteers may have different characteristics from non - volunteers. The sample of volunteers may not be representative of all people who use public Wi - Fi. So the result is very likely not valid because the sample may not be representative of the people who use public Wi - Fi.

Answer:

The probability that at least one of them is careful about personal information is $0.941$.
C. 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.