Question

A website reports that 70% of its users are from outside a certain country, and 60% of its users logon the website every day. Suppose that for its users from inside the country, that 80% of them log onevery day. What is the probability that a person is from the country given that he logs on the websiteevery day? Has the probability that he is from the country increased or decreased with the additionalinformation?

Answer 1

Answer:

The value is $P (I | L ) = 0.63$

The probability has increased

Step-by-step explanation:

From the question we are told that

   The percentage that are from outside the country is  $P(O) = 0.70$

    The  percentage that logs on everyday is  $P(L) = 0.60$

    The  percentage that logs on everyday that are from the inside the country is     $P(L | I) = 0.80$

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

     $P (I | L ) = \frac{P(I)* P(L|I)}{ P(O) *P(L|O) + P(I) *P(L|I) }$

Where  $P(I)$ is the percentage that are from inside that country which is mathematically represented as

       $P(I) = 1 - P(O)$

      $P(I) = 1 - 0.70$

      $P(I) = 0.30$

And $P(L| O)$ is  percentage that logs on everyday that are from the outside  the country which is evaluated as

      $P(L| O) = 1- P(L| I)$

       $P(L| O) = 1- 0.80$

       $P(L| O) = 0.20$

$P (I | L ) = \frac{ 0.3* 0.80 }{ 0.7 *0.20 + 0.3 * 0.8 }$    

$P (I | L ) = 0.63$

Given that the percentage that are from inside that country is  $P(I) = 0.30$

and that the probability that a person is from the country given that he logs on the website every day is  $P (I | L ) = 0.63$

We see that the additional information increased the probability