I have been given a two pronged problem to solve at college whereby I need to calculate the percentages involved in winning a game with a weighted coin.
The game is the be the first to score 5 successes and the coin is weighted 70/30 in favour of heads.
First part is:
How would I go about calculating the possible scorelines involved and the percentage chances of either side winning this game?
I have tried using binomial distribution by drawing out a map and checking off potential scorelines but get confused when having to nullify branches of the tree that are essentially out of play (becuase the goal of 5 has already been reached).
Is there a more simple approach to working out percentages for all possible scorelines and the chances of winning the games?
The Second and more tricky part is:
How do I calculate the percentage chance of either side winning in any given scoreline?
So for example if it is 3-1 to Heads or they are drawing 4-4 , what are the chances of either side winning now?
Any help would be appreciated