Probability of consecutive events in a set

[Jeffery777]

Id really like to know the answer and formula to the following:

Event A has a 55% chance of occurring each permutation and each permutation is independent of one another.

What are the odds of 35 consecutive event A's occurring out of a set of 88 permutations? And what's the formula name for this? I can only find examples online of this problem without the consecutive component included.
Thanks!

 

[pka]

Event A has a 55% chance of occurring each permutation and each permutation is independent of one another.
What are the odds of 35 consecutive event A's occurring out of a set of 88 permutations? And what's the formula name for this? I can only find examples online of this problem without the consecutive component included.

How are you using the word PERMUTATION (please look at the link). It has a very specific meaning is counting theory: "an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements." This is so much part of my work, I just cannot understand your question.

 

[Jeffery777]

perhaps I used incorrectly. At the end of the day I wanted to know the odds of an independent event that has a 55% chance of occurring each instance to occur 35 times in a row anywhere in a set of 88 instances of that event.

 

[Steven G]

Id really like to know the answer and formula to the following:

Hi,
This is a math help forum where we help students, not do their work for them. Please read our guidelines, follow them and post back showing your work and where you are stuck.

 

[Dr.Peterson]

I wanted to know the odds of an independent event that has a 55% chance of occurring each instance to occur 35 times in a row anywhere in a set of 88 instances of that event.

Would you like the probability of exactly 35 in a row (exactly once in the 88!), or at least 35 in a row? Typically the latter would be what you need in order to, say, win a bet, or describe how unlikely an event is.

You're right that this is harder than it would be without the consecutivity requirement; that would be a binomial distribution. I don't see an easy formula to calculate your probability (either way) by hand, but it wouldn't be too hard with a spreadsheet or other technology.

I'm guessing this is not an assignment for a class; it may help us if you tell us the reason for your interest. (Context can also determine the right interpretation of what you are asking.)

 

[pka]

At the end of the day I wanted to know the odds of an independent event that has a 55% chance of occurring each instance to occur 35 times in a row anywhere in a set of 88 instances of that event.

If one flips a coin thirty-five times the probability of all heads is \(\left(\dfrac{1}{2}\right)^{35}=2.910383045673370361328125 × 10^{-11}\) SEE how small That is just thirty five heads in a row. In your case it is \((0.55)^{35}.\) close to the same..
If we flip a coin eighty-eight times there are \(2^{88}\) possible outcomes. It seems you are asking about the probability of there being thirty-five heads in a row. The exact answer is a counting nightmare. So suppose that events \(A~\&~B\) are independent and exhaustive. If \(\mathcal{P}(A)=0.55\) then it must be \(\mathcal{P}(B)=0.45\).
Suppose we have a string looks like \(U:BAA\cdots AAB\), a \(B\) followed by thirty-five \(A's\) followed by a \(B\).
Here goes: of the \(2^{88}\) possible strings of \(A's\text{ or }B's\) contain a the string \(U\) as a sub-srting?
Now the probability of \(\mathcal{P}(U)=(0.55)^{35}(.45)^2\) So I hope you see what I mean by a counting nightmare??