Question

Based on a poll, 68% 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? and how is the result affected by the additional information that the survey subjects volunteered to respond?

Answer 1

Answer:

Here , the no. of individual selected are : n = 4

Probability( Internet users are more careful about personal information when using a public Wi-Fi hotspot) :  P = 0.68  

∵ P(X < 1) = P(0 ≤ X ≤ 1) = P(X=0)

P(X≥1) = 1 - P(X< 1)

∴

P(X) = $\binom{n}{0}\times P^0\times (1-P)^n$

P(X=0) = $\binom{4}{0}\times (0.68)^0\times (1 - 0.68)^n$

P(X=0) ≈0.0140

P(X<1) = 0.0105

P(X≥1) = 1 - P(X< 1)

P(X≥1) = 1 - 0.0105 = 0.9895

The result is affected by the additional information that the survey subjects volunteered to respond as self selection causes the survey to be biased towards people with stronger opinion.