Answer:
The value is [tex]P (I | L ) = 0.63[/tex]
The probability has increased
Step-by-step explanation:
From the question we are told that
The percentage that are from outside the country is [tex]P(O) = 0.70[/tex]
The percentage that logs on everyday is [tex]P(L) = 0.60[/tex]
The percentage that logs on everyday that are from the inside the country is [tex]P(L | I) = 0.80[/tex]
Generally using Bayes' Rule the probability that a person is from the country given that he logs on the website every day is mathematically represented as
[tex]P (I | L ) = \frac{P(I)* P(L|I)}{ P(O) *P(L|O) + P(I) *P(L|I) }[/tex]
Where [tex]P(I)[/tex] is the percentage that are from inside that country which is mathematically represented as
[tex]P(I) = 1 - P(O)[/tex]
[tex]P(I) = 1 - 0.70[/tex]
[tex]P(I) = 0.30[/tex]
And [tex]P(L| O)[/tex] is percentage that logs on everyday that are from the outside the country which is evaluated as
[tex]P(L| O) = 1- P(L| I)[/tex]
[tex]P(L| O) = 1- 0.80[/tex]
[tex]P(L| O) = 0.20[/tex]
[tex]P (I | L ) = \frac{ 0.3* 0.80 }{ 0.7 *0.20 + 0.3 * 0.8 }[/tex]
[tex]P (I | L ) = 0.63[/tex]
Given that the percentage that are from inside that country is [tex]P(I) = 0.30[/tex]
and that the probability that a person is from the country given that he logs on the website every day is [tex]P (I | L ) = 0.63[/tex]
We see that the additional information increased the probability
