Formula to calculate the probability of the next value, considering previous pattern

Hello,

I was hoping somebody could help me with a formula...


I have two columns A (where the only values that will be entered are "apple" and "peach") and B. I need a formula to enter in cells of column B that will return the following values: what is the probability of "apple" and "peach" to be the next value in column A, considering the previous "pattern" from column A? Consider the case attached.


Thank you!

I will first admit that my stats/probability skills are quite inadequate. daddylonlegs and martindwilson's response is correct for a true binomial experiment -- the result of one trial cannot effect the result of any other trial. It would appear to me that at the heart of the question is "how can one determine if each trial of an experiment is truly independent." My stat knowledge doesn't go that far. I suspect that, in order to do this rigorously, you need to take this question to some statisticians and see how they would do it. I fully expect that the science of statistics has developed algorithms for testing these kinds of patterns in order to test the validity of an experiment that claims to be binomial.

I doubt this is rigorous, but a starting point might be to look at pairs of trials. There are four possibilities: apple followed by apple, apple then peach, peach then apple, peach then peach. If the trials are independent, then you'd expect the probability of each combination to be 1/4.

1/(2^2) = 25% is the general answer, but your question doesn't provide enough information for a proper statistical experiment.....