Answer:
To solve this problem, we can use the complementary probability approach, which means finding the probability of the opposite event and then subtracting it from 1.
Let A be the event that an Internet user is more careful about personal information when using a public Wi-Fi hotspot, and let A' be the event that an Internet user is not more careful about personal information when using a public Wi-Fi hotspot.
The probability of A is 0.65, so the probability of A' is 1 - 0.65 = 0.35.
To find the probability that at least one of the three randomly selected Internet users is more careful about personal information when using a public Wi-Fi hotspot, we need to find the probability of the event A happening at least once in three independent trials.
Using the complementary probability approach, the probability of none of the three users being more careful about personal information is (0.35)^3 = 0.042875.
Therefore, the probability that at least one of the three users is more careful about personal information is:
1 - 0.042875 = 0.957125
So, the probability that among the three randomly selected Internet users, at least one is more careful about personal information when using a public Wi-Fi hotspot is approximately 0.957 or 95.7%