Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

when you draw this graph how can you sure that state go from 1 to 2 is 100%?

look at first example, there is a p and q is it probability from 1 to 2 that is drawn only when P(from 1 to 2) > 0.5, such as p = 0.8?

look at example For [6], d(1) = g.c.d.{3, 5, 6, ..} = 1 1 -> 2 -> 3 -> 1, then there is 3, will above consideration change this calculation? what is the relationship between using this p and q and gcd?

share|cite|improve this question

On the first chain


the transition probability from 1 to 2 is found next to the arrow pointing from 1 to 2. This probability is denoted by $b$. If $b<1$, the probability of going from 1 to 2 is less than 100%.

On the 5th and 6th chains


the only arrow leaving 1 is the arrow toward 2. Although probabilities are not specified, the absence of arrows from 1 to 1, 3 or 4 means that the corresponding transitions have probability zero. The probability of going from 1 to 2 is equal to $1$ (or 100% if you prefer).

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.