1. ## Probability Problem

A random sample of a automatic hole punching machine, found that it punched a hole in the correct location (A) and an incorrect location (B) in the following fashion:

AAAAABBAAAAAAAAAABAAAAAAAAAABAAAA

What is the probability that the next punched hole location will be A?
What is the probability that the next punched hole location will be B?

2. ## Re: Probability Problem

Since this is advanced statistics, what methodology are you using? Are pairs of incorrect punches significant to this methodology? Now, a pre-university statistics class would not give you a methodology and would simply expect you to count the number of correct punches and the number of incorrect punches. The expectation for a correct punch as the next punch is the number of correct punches divided by the total number of punches in the sample. The probability of an incorrect punch would be the total number of incorrect punches divided by the total number of punches in the sample. But that is not advanced statistics.

3. ## Re: Probability Problem

Thanks SlipEternal

The problem needs to incorporate the knowledge that there are many more A's than B's.....no other pattern taken into account. I think maybe Bayes theorem. Just not sure how to apply Bayes theorem to this one.

4. ## Re: Probability Problem

Thanks, I'll take a look when I have a moment

5. ## Re: Probability Problem

$P(A) = \dfrac{29}{33}$
$P(B) = \dfrac{4}{33}$
$P(A|A) = \dfrac{26}{29}$
$P(A|B) = \dfrac{3}{4}$
$P(B|A) = \dfrac{3}{29}$
$P(B|B) = \dfrac{1}{4}$

You will want a setup something like this (I may have gotten it wrong because I am very tired). The idea is, the probability that A will follow an A is much higher than the probability that B will follow an A.

You need to continue to find larger pattern, building a tree diagram, IIRC.