Question

You could win a $1000 prize by tossing a coin in one of two games: game
a.to win you must get exactly 50% heads game
b.to win you must get between 45% and 55% heads although which game you must play will be chosen randomly, then you may decide whether to toss the coin 20 times or 50 times. how many tosses would you choose in order to maximize your chances of winning the game?

Answer 1

In either game, 50 tosses would increase your chances of winning.  

The theoretical probability of flipping heads is 1/2 or 50%.  The more times you perform an experiment, the closer the experimental probability is to the theoretical.  This means that your average will be closer to 50% the more times you perform the experiment.