I am trying to work out the probabilities of losing a game of chance (1 in 2 chance per game) by sticking with the same answer, say heads on a coin toss.
I know there is a 1 in 2 chance of tails on the first game, then 1 of 2 possible outcomes again on the second game, and 3rd etc, but the chance of the same outcome repetitively is multiplied by the chance of each occurrence. So 2nd time 1/2 * 1/2 = 1/4, then 1/8 etc.
What I'm not sure about is, if that's the chance for each game, is the chance of losing all games multiplied together?
So to lose the first and second games you would need to multiply the 1/2 and 1/4 together giving 1/8, and to also lose the 3rd game you would also multiply by the 1/8 chance for that game. Giving 1/64. Chances for the 3rd game are a 1/8 chance of losing by sticking with heads following 2 tails outcomes, but are the chances of losing all 3 games 1 in 64?
It's 15 years since I did statistics in school and by the 4th game this gives 1/976, which seems too high to me, 1/16 seems more realistic, if anyone has a better understanding than me their input would be appreciated.