What Is the Value of a(16) When No Two Heads Occur Consecutively in Coin Tosses?

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Homework Help Overview

The discussion revolves around determining the value of a(16) in the context of tossing a fair coin 'n' times, with the condition that no two heads occur consecutively. Participants are exploring the combinatorial aspects of this problem.

Discussion Character

  • Exploratory, Assumption checking, Mixed

Approaches and Questions Raised

  • Some participants suggest using recurrence relations to approach the problem, while others mention the potential use of Markov Chains. There are also questions regarding the relevance of the problem to schoolwork and the motivations behind the thread.

Discussion Status

The discussion has seen various attempts to engage with the problem, but there is a notable lack of consensus on the direction or purpose of the thread. Some participants express frustration over perceived condescension and the clarity of the discussion.

Contextual Notes

There are indications of prior knowledge among some participants, which raises questions about the intent of the original poster and the overall purpose of the thread. Additionally, the thread has been moved from another section, which may affect the context of the discussion.

Cosmos
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Mod note: Thread moved from technical math section, so homework template does not appear.
A fair coin is tossed 'n' times. Let a(n) denote the number of cases in which no two heads occur consecutively, then what is the value of a(16)?:woot:
 
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Cosmos said:
A fair coin is tossed 'n' times. Let a(n) denote the number of cases in which no two heads occur consecutively, then what is the value of a(16)?:woot:
What do you think it is? What are the Relevant Equations? Is this a question from your schoolwork?
 
No...But it involves a good trick (i think) instead of simply rather foolishly counting...:-p
 
Cosmos said:
No...But it involves a good trick (i think) instead of simply rather foolishly counting...:-p
Are you saying that you already know the answer?
 
Cosmos said:
A fair coin is tossed 'n' times. Let a(n) denote the number of cases in which no two heads occur consecutively, then what is the value of a(16)?:woot:
Doing it with a recurrence turns out very nicely.
 
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Markov Chains also work pretty nicely.
 
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phinds said:
Are you saying that you already know the answer?
yes my boy
 
So what is the point of this thread?

~4% probability.
 
mfb said:
So what is the point of this thread?
My point exactly.
Cosmos said:
yes my boy
I do not appreciate the smarmy answer and if you know the solution then I agree with mfb. What's the point of this thread?
 
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  • #10
phinds said:
What's the point of this thread?

Thus far the point has been "I know something you don't, nyah nyah nyah!" I certainly hope there is more to it soon.
 
  • #11
Vanadium 50 said:
Thus far the point has been "I know something you don't, nyah nyah nyah!" I certainly hope there is more to it soon.
You don't really expect for there to be do you? I think you've already nailed it.
 
  • #12
Mod note: Edited post to remove insulting and condescending contents.
mfb said:
So what is the point of this thread?

~4% probability.
I know the 'ANSWER' but i don't know the 'SOLUTION'...:cool:...and i do hope for a very good method to get it...:wink:...
 
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  • #13
OK, then this should be treated as any homework problem. So what have you tried?
 
  • #14
Cosmos said:
yes my boy

phinds said:
My point exactly.

I do not appreciate the smarmy answer
Nor do I. The OP has earned an infraction for this.
 
  • #15
so
phinds said:
My point exactly.

I do not appreciate the smarmy answer and if you know the solution then I agree with mfb. What's the point of this thread?
sorry sir:bow:
 
  • #16
This is going nowhere. Thread closed.
 

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