text: user6829: I am reading "Statistical methods in bioinformatics"
  I came across this formula:
  
  As explained in the book O are the observations:
   
  My question is why the author only specified $prob(O)$ for a sequence of length=1 ?, I assume he is only talking about one observation, but generally we have a sequence $O_1 ,O_2,O_3,...$. 
  I assume that $Prob(sequence)= P(O_1).P(O_2)...$ but I am not sure.
  
  user2108: The author writes in the quote that $O$ is to be taken for the whole set of positions $O_{i}$.
  In the extracts that you provide there is no reason to believe that it is only for a sequence of length 1. The author writes "the observed sequence $O = O_1, O_2...$"
  Thus as you say $Pr(sequence) = Pr(O) = Pr(O_1) * Pr(O_2)...$ according to my understanding of the quotes.
  
original_text: 6829: <p>I am reading "<code>Statistical methods in bioinformatics</code>"</p>
  
  <p>I came across this formula:
  <a href="https://i.stack.imgur.com/eSebp.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/eSebp.png" alt="enter image description here"></a></p>
  
  <p>As explained in the book <strong>O</strong> are the observations:
  <a href="https://i.stack.imgur.com/DnIgr.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/DnIgr.png" alt="enter image description here"></a> </p>
  
  <p>My question is why the author only specified <span class="math-container">$prob(O)$</span> for a sequence of length=1 ?, I assume he is only talking about one observation, but generally we have a sequence <span class="math-container">$O_1 ,O_2,O_3,...$</span>. </p>
  
  <p>I assume that <span class="math-container">$Prob(sequence)= P(O_1).P(O_2)...$</span> but I am not sure.</p>
   2108: <p>The author writes in the quote that <span class="math-container">$O$</span> is to be taken for the whole set of positions <span class="math-container">$O_{i}$</span>.</p>
  <p>In the extracts that you provide there is no reason to believe that it is only for a sequence of length 1. The author writes &quot;the observed sequence <span class="math-container">$O = O_1, O_2...$</span>&quot;</p>
  <p>Thus as you say <span class="math-container">$Pr(sequence) = Pr(O) = Pr(O_1) * Pr(O_2)...$</span> according to my understanding of the quotes.</p>
  