Bayes formula:

Conditioning on a variable (useful if I don't know P(B) but know the stuff on the right side of the equation):

Problem

There are 10282 students at the university, out of whom 80 are on the 2nd year of Informatics. 50% of 2nd year Informatics students know Bayes theorem, out of the rest of the students 5% know it.

A student was randomly chosen and asked if they know the Bayes theorem. The answer was "Yes". Calculate the probability that this was a 2nd year Informatics student.

What are we looking for?

Random variables:

• IAIB3IAIB3 - student is 2nd year Informatics student (yes/no)
• KnowsBayesKnowsBayes - knows Bayes theorem (yes/no)

Need to find P(IAIB3=yes|KnowsBayes=yes)P(IAIB3=yes|KnowsBayes=yes)

First we need the initial data from the text. Use values in the range 0-1 to represent probabilities.

What is the value of P(KnowsBayes=yes|IAIB3=yes) given in the text?