Based on a poll, 66% 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?

98.66% probability that among four randomly selected Internet users, at least one is more careful about personal information when using a public Wi-Fi hotspot

Step-by-step explanation:

For each internet user, there are only two possible outcomes. EIther they are more careful about personal information when using a public Wi-Fi hotspot, or they are not. The probability of an internet user being more careful about personal information when using a public Wi-Fi hotspot is independent of other users. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

66% of Internet users are more careful about personal information when using a public Wi-Fi hotspot.

This means that

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?

This is when n = 4.

We know that either none of them are more careful, or at least one is. The sum of the probabilities of these events is decimal 1. So

In which

98.66% probability that among four randomly selected Internet users, at least one is more careful about personal information when using a public Wi-Fi hotspot

the answer is b.)

< 1=< 2