On your way to the hotel you discover that the National Basketball Player's Association is having a convention in town and the official hotel is the one where you are to stay, and furthermore, they have reserved all the rooms but yours.The whole idea is to consider the joint probability of both events, A and B, happening together (a man over 5'10" who plays in the NBA), and then perform some arithmetic on that relationship to provide a updated (posterior) estimate of a prior probability statement.Take this information into account in your prior and calculate new posterior. $Y$ is 2 here, $N=18$ but why is that $r$ in the equation?
Bayesian inference is an important technique in statistics, and especially in mathematical statistics.
Each red ball you see then makes it more likely that the next ball will be red, following a Laplacian Rule of Succession.
For example, seeing 6 red balls out of 10 suggests that the initial probability used for assigning the balls a red color was .6, and that there's also a probability of .6 for the next ball being red.
What values should I give $α$ and $β$ to take into account prior information? A general lecture on prior and posterior distributions wouldn't hurt either (I have vague understanding what they are but only vague) Also bear in mind I'm not very advanced statistician (actually I'm a political scientist by my main trade) so advanced mathematics will probably fly over my head.
The phrase "Find the posterior distribution of left-handed students" makes no sense.