Question

help solve this problem Based on a​ poll, 62​% 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? How is the result affected by the additional information that the survey subjects volunteered to​ respond?

Answer 1

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 is 0.979.

Explanation:

Since 62​% of Internet users are more careful about personal information when using a public​ Wi-Fi hotspot.

Therefore, the Probability of 62​% of Internet users are more careful about personal information when using a public​ Wi-Fi hotspot is, p=0.62.

We have to find the probability that at least one user is more careful about personal information when using wi-fi hotspot.

Probability of internet users are not more careful about personal information when using a public wi-fi hotspot, i.e
`q=1-p`

`q=1-0.62=0.38`

Use Binomial Distribution, i.e,
`P\left ( X \right )=^nC_xp^xq^\left ( n-x \right )`

p=0.62, q=0.38, n=4.

Required Probability
`P\left ( X\geq 1 \right )=P\left ( X=1 \right )+P\left ( X=2 \right )+P\left ( X=3 \right )+P\left ( X=4 \right )`

or

`P\left ( X\geq 1 \right )=1-P\left ( X=0 \right )`

=1-
`^4C_0p^0q^\left ( 4-0 \right )`

=1-
`4\cdot1\cdot q^\left ( 4-0 \right )`

=1-
`4\cdot \left ( 0.38 \right )^4`

=1-0.02085136=0.97914864

Therefore, the probability that at least one users more careful about personal information when using wi-fi hotspot, i.e 0.979(approx).

RESULT:

The result should not be impacted by this because volunteers are likely to have the most relevant responds.