A website reports that 80% of its users are from outside a certain country Of th

Question

A website reports that 80% of its users are from outside a certain country Of the users from the country, one-seventh log on every day. Of the users from other countries. one-eleventh tog on every day. What is the probability that a user is from the country given that ho logs on to the website every day? Hat the probability that he is from the country increased or decreased with the additional information? Select the correct choice below and fill in the answer box within that choice. The probability that a user is from the country has increased with the additional information that he logs on every day because the from the country given that ho togs on to the website every day is which is greater than the probability that he is from the country. (Round to two decimal places as needed)

Explanation / Answer

Let

O = from outisde the country
I = inside the country
L = logs on everyday

hence, by Bayes' Rule,

P(L) = P(O) P(L|O) + P(I) P(L|I) = 0.80*(1/11) + (1-0.80)*(1/7) = 0.101298701

hence,

P(I|L) = P(I) P(L|I)/P(L) = (1-0.80)*(1/7)/0.101298701 = 0.282051283 [ANSWER]

As P(I) = 1 - 0.80 = 0.20, then we see that the probability increased.

So,

ANSWER: OPTION A: 0.282051283 [ANSWER]

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