Pascal: The proverbial coin toss.

[schema]

I should preface this question by saying that I am a computer science major.

A logic question was posed in an IT class as a challenge. It is extra-curricular and pertains very little to actual subject matter. The question, I assume, was a 'satirical' reference to the pascal language, or perhaps binary code. None of us are math majors, obviously, so hence the challenge. I think our proctor was hinting that we should program a script to solve this, which i intend to do. I just need some guidance in how I find the method in which I can deduce a solution.

We were give 2 sequences of flips (HT) and asked to compare the probabilities of the sequences.I immediately thought of the pascal triangle, which i think is a step in the right direction. However, one of the sequences is repeating while the other is seemingly random:

e.g. HTHTHTHHTHTHTHTHTH
HHHHHHHHTTTTTTTTTT

My question is, do I approach this by mapping this out with pascal triangle and just taking the probability of H in each sequence, or do i need to apply another method to take into account the repeating sequence?

 

[mathman]

Maybe I don't understand the question. However any specific sequence has a probability (assuming a fair coin) of (1/2)ⁿ, where n is the number of tosses.

 

[schema]

thank you. that is more direct and simple than I thought.

 

[Stephen Tashi]

and asked to compare the probabilities of the sequences.

There are other ways to "compare" two probabilities than by computing each probability. We should first determine whether your instructor said to "compare" them or to "compute" them.

Two sequences of independent flips of a fair coin have the same probability if they have the same length.

 

[schema]

There are other ways to "compare" two probabilities than by computing each probability. We should first determine whether your instructor said to "compare" them or to "compute" them.

Two sequences of independent flips of a fair coin have the same probability if they have the same length.

The directive was to find "how much more probable" one was to the other. I didn't know if the sequence repetition played a part in how to find the solution.

thank you for the help. this is not my area of expertise.

 

[awkward]

Maybe I don't understand the question. However any specific sequence has a probability (assuming a fair coin) of (1/2)ⁿ, where n is the number of tosses.

That's assuming independence, which seems questionable in both the examples given.

 

[Stephen Tashi]

That's assuming independence, which seems questionable in both the examples given.

The problem could be investigated not assuming a fair coin or not assuming independence if we take a Bayesian point of view. But if we take that point of view, a problem posed by an instructor not teaching a class in Bayesian statistics probably should be solved by assuming independence and a fair coin.