Question

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?

Answer 1

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.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

$C_{n,x} = \frac{n!}{x!(n-x)!}$

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 $p = 0.66$

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 $P(X \geq 1)$ 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

$P(X = 0) + P(X \geq 1) = 1$

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{4,0}.(0.66)^{0}.(0.34)^{4} = 0.0134$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0134 = 0.9866$

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

Answer 2

Answer:

The probability that at least one internet user is more careful is 0.973

Step-by-step explanation: