Markov plays a game for three turns. On each turn, he either rolls a fair, six sided die or flips a fair coin. If he rolls a 1 or 2 on the die, he will switch to the coin on the next turn, and if he flips a tails on the coin, he will switch to the die on the next turn. If Markov starts by rolling the die, what is the probability that he will flip the coin on the third turn?

The probability would be 2/9.

If he starts by rolling the die and does not flip the coin the second turn, then he must not have rolled a 1 or a 2 on the first turn. The probability of this happening is 4/6 or 2/3.

She would then roll the die again, but this time she will get a 1 or a 2 on the die; the probability of this happening is 2/6 = 1/3.

The total probability is given by 2/3 (1/3) = 2/9.