AdvancedNumeric answer
The dragon with regrowing heads · Part 3 of 3
A dragon starts with 3 heads. Each swing has a 20% chance to remove 2 heads permanently, a 60% chance to remove 1 head that regrows before the next swing, and a 20% chance to add 1 head. At 0 heads you win; at 5 heads you lose. From 1 head, a two-head strike kills the dragon, while a one-head strike regrows it. All swings are independent.
The interviewer changes only the one-head rule: a shallow strike at 1 head now kills the dragon instead of regrowing it. What is the new probability of winning from 3 heads? Give an exact fraction or decimal.
Answer with a number. Fractions, powers and expressions like 23/6 or C(52,5) are read correctly in practice.
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