Diane Has Decided to Play the Following Game of Chance

question 172

Essay

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.

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Definitions:

Combinations

A mathematical technique to determine the total possible arrangements of a set of items where the order of the items does not matter.

Factorial Designs

A statistical analysis method that allows researchers to study the effects of two or more independent variables on a dependent variable simultaneously.

Single-Factor Designs

Experiments that investigate the effect of one independent variable on one or more dependent variables.

Interaction Effects

The impact on a dependent variable that changes depending on the levels of two or more independent variables.