Question

In the casino version of the traditional Australian game of two-up, a spinner stands in a ring and tosses two coins into the air. The coins may land showing two heads, two tails, or one head and one tail (odds). Players can bet on either heads or tails at odds of one to one. Therefore, if a player bets $1 on heads, the player will win $1 if the coins land on heads but lose $1 if the coins 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 if the coins land on heads. If the coins land on odds, all bets are frozen and the spinner tosses again until either heads or tails comes up. If five odds are tossed in a row all players lose.

(a) Construct the probability distribution respresenting the different outcomes that are possible for a $1 bet on heads.

(b) Construct the probability distribution respresenting the different outcomes that are possible for a $1 bet on tails.

(c) What is the expected long-run profit (or loss) to the player?

Answer 1

when two coins are flipped the outcomes are (HH),(TT),(HT) and (TH)

each outcome has a probability of 1/4.

A)

Probability distribution representing different outcomes that are possible for a $1 bet on heads .

we get $1 when (HH) is the outcome therefore probability of getting$1 is 1/4

we loss when(TT) is the outcome therefore probability of getting -$1 is 1/4

we get $0 when (HT) and (TH) are the outcomes therefore probability of getting $0 is 1/2.

X(money we get)	+1	0	-1
probability p(x)	1/4	1/2	1/4

B)

Probability distribution representing different outcomes that are possible for a $1 bet on tails.

we get $1 when (TT) is the outcome therefore probability of getting$1 is 1/4

we loss when(HH) is the outcome therefore probability of getting -$1 is 1/4

we get $0 when (HT) and (TH) are the outcomes therefore probability of getting $0 is 1/2.

X(money we get)	+1	0	-1
probability p(x)	1/4	1/2	1/4

C)

Expectd long run profit or loss is

Expected long run profit = $0