Diane has decided to play the following game of chance. She places a $1 bet on each repeated play of the game in which the probability of her winning $1 is 0.5. She has further decided to continue playing the game until she has either accumulated a total of $3 or has lost all her money.
What is the probability that Diane will eventually leave the game a winner if she started with a capital of $1?
What is the probability that Diane will eventually leave the game a winner if she started with a capital of $2?
Write your answer as a decimal rounded to two decimal places.

Question

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The Answer of Diane has decided to play the following game of chance. She places a $1 bet on each repeated play of the game in which the probability of her winning $1 is 0.5. She has further decided to continue playing the game until she has either accumulated a total of $3 or has lost all her money.
What is the probability that Diane will eventually leave the game a winner if she started with a capital of $1?
What is the probability that Diane will eventually leave the game a winner if she started with a capital of $2?
Write your answer as a decimal rounded to two decimal places.

Diane Has Decided to Play the Following Game of Chance