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

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The discussion revolves around finding the value of a(16), which represents the number of ways to toss a fair coin 'n' times without getting two heads consecutively. Participants express frustration over the lack of constructive dialogue, with some indicating they already know the answer but seek a solution method. Recurrence relations and Markov Chains are mentioned as effective approaches to solve the problem. The conversation becomes contentious, with accusations of condescension and a lack of meaningful contribution. Ultimately, the thread is closed due to unproductive exchanges.
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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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