Each day Alice and Bob flip a coin to see who buys coffee ($1.20 a cup). Bob flips and Alice calls the outcome. If the person who calls the outcome is correct, the other buys the coffee;otherwise the caller pays.
(a) Determine Alice’s expected winnings if a fair coin is used and she calls the outcomes at random. Does Bob have an advantage if he decides to use a biased coin? Motivate your answer.
(b) Ignoring your advice, Bob decides to cheat with a biased coin that results in heads 2/3 of the time. Suspecting this, Alice decides to change her strategy as well to one where she guesses heads 75% of the time. Over the course of 100 days, how many times do you expect Alice to win a cup of coffee?
I'm not sure what direction to go in with this one! Please help!!!