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 . (round to three decimal places as needed.)

Explanation:

Step1: Find the probability that none are careful

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

Step2: Find the probability that at least one is careful

The probability that at least one is more careful about personal information is the complement of the event that none are careful. Let $P(X\geq1)$ be the probability that at least one is careful. Then $P(X\geq1)=1 - P(X = 0)$.
$P(X\geq1)=1 - 0.059319 = 0.941$.

Answer:

$0.941$