Start - State 0
Flip a Tails = Stay in State 0 probability is 50%
Flip a Heads = Move to State 1 probability is 50%
Next?
Question:
A coin is tossed until five consecutive heads appear. Model this process as a Markov chain where the states are the numbers of consecutive heads. (0,1,...,5).
a. Find the probability that it takes 10 or fewer tosses to observe five consecutive heads.
b. Find the mean number of tosses it takes to obtain five consecutive heads.
What I know - the probability of getting 5 H in a row is 1/32
I also know I shouldn't be confused about this, but I'm missing something.
Can you help?
Thanks for answering. So, if I flip a tails I have to start again, right? But if I get heads I flip again and I either end up with a tails and have to start again or get heads and keep going. How do I summarize this in a chart does it have 0-10 on the top and on the side and then just work on the probabilities within it?
The states are 0,1,2,3,4,5 the probability of transition from n to state n+1, n=0,1,2,3,4 is 0.5,from state n to state 0 , n=1,2,3,4 is 0.5. State 5 is absorbing (the transition probability from 5 to 5 is 1),the transition probability from state 0 to state 0 is 0.5. All other transition probabilities are 0.
Now write this as a transition matrix.
CB