Question

Based on a​ poll, 6767​% 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?

What is the probability that at least one of them is careful about personal information is? (Round answer to nearest 3 decimal place if needed)

Answer 1

X ~ Bin ( n , p)

Where n = 4 , p = 0.67

Binomial probability distribution is

P(X) = ⁿC_x * p^x * ( 1 - p)^n-x

P(X >= 1) = 1 - P(X = 0)

= 1 - ⁴C₀ * 0.67⁰ * ( 1 - 0.67)⁴

= 0.988

With the additional information, it is possible that the result is not valid because sample may not be

representative of the people who use public Wi-Fi