You play a game of dice where you roll a fair 6-sided die, continue playing if you roll a 4 or lower, and stop if you roll a 5 or higher. What's the probability that you're still playing after 3 rolls?
Is this the right way to approach the game?
When i roll a 1 then i can roll the dice for 2,3,4 when i roll a 2 then i can roll the dice for 1,3,4 when i roll a 3 then i can roll the dice for 1,2,4 when i roll a 4 then i can roll the dice for 1,2,3
the probability of still playing after 3 rolls is 1/6(1+2+3+4) ?