A ...........................
Answer:
The value is ![P (I | L ) = 0.63](https://tex.z-dn.net/?f=P%20%28I%20%7C%20%20L%20%20%29%20%20%3D%20%20%20%20%200.63)
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](https://tex.z-dn.net/?f=P%28O%29%20%3D%20%200.70)
The percentage that logs on everyday is ![P(L) = 0.60](https://tex.z-dn.net/?f=P%28L%29%20%3D%20%200.60)
The percentage that logs on everyday that are from the inside the country is ![P(L | I) = 0.80](https://tex.z-dn.net/?f=P%28L%20%20%7C%20%20I%29%20%3D%20%200.80)
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) }](https://tex.z-dn.net/?f=P%20%28I%20%7C%20%20L%20%20%29%20%20%3D%20%20%5Cfrac%7BP%28I%29%2A%20P%28L%7CI%29%7D%7B%20P%28O%29%20%2AP%28L%7CO%29%20%2B%20P%28I%29%20%2AP%28L%7CI%29%20%7D)
Where
is the percentage that are from inside that country which is mathematically represented as
![P(I) = 1 - P(O)](https://tex.z-dn.net/?f=P%28I%29%20%3D%20%201%20-%20%20P%28O%29)
![P(I) = 1 - 0.70](https://tex.z-dn.net/?f=P%28I%29%20%3D%20%201%20-%20%200.70)
![P(I) = 0.30](https://tex.z-dn.net/?f=P%28I%29%20%3D%20%200.30)
And
is percentage that logs on everyday that are from the outside the country which is evaluated as
![P(L| O) = 1- P(L| I)](https://tex.z-dn.net/?f=P%28L%7C%20O%29%20%20%3D%20%201-%20%20P%28L%7C%20I%29)
![P(L| O) = 1- 0.80](https://tex.z-dn.net/?f=P%28L%7C%20O%29%20%20%3D%20%201-%20%200.80)
![P(L| O) = 0.20](https://tex.z-dn.net/?f=P%28L%7C%20O%29%20%20%3D%200.20)
![P (I | L ) = 0.63](https://tex.z-dn.net/?f=P%20%28I%20%7C%20%20L%20%20%29%20%20%3D%20%20%20%20%200.63)
Given that the percentage that are from inside that country is ![P(I) = 0.30](https://tex.z-dn.net/?f=P%28I%29%20%3D%20%200.30)
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](https://tex.z-dn.net/?f=P%20%28I%20%7C%20%20L%20%20%29%20%20%3D%20%20%20%20%200.63)
We see that the additional information increased the probability
Answer:
Step-by-step explanation: