Probability of a Goalkeeper being world class.
Hi I'm new to this forum, but I could seriously do with some help guys.
Okay so here's the question
An ordinary goalkeeper has a 20% chance of saving a penalty. A world class goalkeeper has a 40% chance of saving a penalty. One in 10 professional goalskeepers are world- class.
If I saw a goalkeeper saving a penalty, would I think that he was world-class? (I think I have to find P(A[B) using the Bayes' rule, where A is the goalkeeper being world class, and B him saving the penalty)
An additional question is: If he saves the penalty in a row would you then think he was world class?
Another additional question is: If he has 10 penalties taken against him, how many would he have to save for you to be 95% confident that he was world class?
Any help would be great!