4 You play a game with your friend in which you alternate fl

4.) You play a game with your friend in which you alternate flipping a weighted coin, which comes up heads with probability 1 25 . You flip the coin first. The player who flips a heads first wins the game. a.) What is the probability that you win the game? b.) What is the expected value of the number of coin flips it will take to end the game? (Hint: Use a variable! Your answer is when x = 1 25 .)

Solution

a.) What is the probability that you win the game?

P = 1 / 25

What is the expected value of the number of coin flips it will take to end the game?

EXPECTED VALUE WILL BE THE PROBABILITY 1 / 25 MULTIPLY BY THE NUMBER OF HEADS THAT YOU OBTAIN IN THIS GAME

SO

EXPECTED VALUE = 1 / 25 * N

where N = number of heads in the game