In a football game, the sides in the soccer field are determined on the basis of a single coin flip by the referee and the team which correctly guesses the flip result gets its desired side. What is the probability that a team will have to wait until its 8th game to get its desired side?
I am stuck with this question, any help would be much appreciated!
I thought, $\frac{1}{2}^8$ but it is wrong.
it depends. if they play against a team who usually picks the side that 'our' team wants again and again, than they are more likely to wait until their 8th game, but then they might lose the toss again. the other way around is the exact opposite, because if both teams want different sides, than they will probably get their chosen side first game. it's most likely to happen if each team who wins the toss chooses randomly, in which case the chances are still as low as 1/2^16.