Question

Based on a poll, 69% 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 a Wi-Fi hotspot?

a How is the result affected the additional information that the survey subjects to respond?

b. The probability that at least one of them is careful about personal information is.

Answer 1

Answer:

a) If we don't have enough info we can create bias in the results and that's not the idea. and since the experiment is conducted in public WIFI spot probably we have some information that will be not share with other and that probably will create bias in the results.

b) $P(X \geq 1)$

And we can use the complement rule and we have:

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

$P(X=0)=(4C0)(0.69)^0 (1-0.69)^{4-0}=0.00923$

$P(X \geq 1)= 1-P(X<1) =1-P(X=0)=1-0.00923=0.9908$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=4, p=0.69)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

Part a

If we don't have enough info we can create bias in the results and that's not the idea. and since the experiment is conducted in public WIFI spot probably we have some information that will be not share with other and that probably will create bias in the results.

Part b

For this case we want this probability:

$P(X \geq 1)$

And we can use the complement rule and we have:

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

$P(X=0)=(4C0)(0.69)^0 (1-0.69)^{4-0}=0.00923$

$P(X \geq 1)= 1-P(X<1) =1-P(X=0)=1-0.00923=0.9908$