In the casino version of the traditional Australian game oftwo-up, a spinner stands in a ring and tosses two coins into theair. The coins may land showing two heads, two tails, or one headand one tail (odds). Players can bet on either heads or tails atodds of one to one. Therefore, if a player bets $1 on heads, theplayer will win $1 if the coins land on heads but lose $1 if thecoins land on tails. Alternatively, if a player bets $1 on tails,the player will win $1 if the coins land on tails but lose $1 ifthe coins land on heads. If the coins land on odds, all bets arefrozen and the spinner tosses again until either heads or tailscomes up. If five odds are tossed in a row all players lose.
(a) Construct the probability distribution respresenting thedifferent outcomes that are possible for a $1 bet on heads.
(b) Construct the probability distribution respresenting thedifferent outcomes that are possible for a $1 bet on tails.
(c) What is the expected long-run profit (or loss) to theplayer?
