Respuesta :
Answer:
The probability that at least one internet user is more careful is 0.973
Step-by-step explanation:
Answer:
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.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
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 [tex]p = 0.66[/tex]
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 [tex]P(X \geq 1)[/tex] 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
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{4,0}.(0.66)^{0}.(0.34)^{4} = 0.0134[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0134 = 0.9866[/tex]
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
