A die is thrown repeatedly until it lands ‘6’ three times in a row. Model this...

A die is thrown repeatedly until it lands ‘6’ three times in a row. Model this by a Markov chain

Expert Solution

The problem can be modeled as Markov chain with 4 states - '0' , '6', '66' and '666' where

State '0' - State with no '6' on the dice

State '6' - State with a '6' on the dice

State '66' - State with a two '6' on the dice

State '666' - State with a three '6' on the dice. This is a an Absorbing state, which denotes the state when the dice 'lands '6' three times in a row.

The transition probability from state '0' to state '6'; state '6' to state '66'; and state '66' to state '666' is 1/6 (Rolling a 6 on the dice)

The transition probability from state '0' to state '0'; state '6' to state '0'; and state '66' to state '0' is 5/6 (Rolling a number other than 6 on the dice)

The transition probability from state '666' to state '666' is 1. The transition probability from state '666' to any other state is 0.

The transition probability matrix and diagram is,

orchestra answered 1 year ago

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