# Thread: Probability of a Goalkeeper being world class.

1. ## 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!

2. Originally Posted by IronMan
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)

$P(WC|S)= \frac{P(S|WC)P(WC)}{P(S)}=\frac{0.4\times 0.1}{0.4\times 0.1+0.2 \times 0.9}$

RonL

3. Originally Posted by IronMan
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!

For the later parts of this question you need to be able to claculate the
probability of a keeper saving $N$ from $M$ penalties given the probability of
saving a single penalty $p$.

The number saved from $M$ has a binomial distribution so:

$P(N,M)=b(N;M,p)$

RonL