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The traditional Australian game of 'Two-Up' involves tossing two coins. Players can bet either on two heads (HH) or two tails (TT). If a head and a tail is thrown (HT or TH), the player continues tossing until either HH or TT results. If 5 successive tosses result in a
H and
T, all bets loose, and the game is finished.
Using your table from Question (3), answer the following questions:
(a) Find the probability that the game finishes on the first toss. Explain your answer.
(2 marks)

The traditional Australian game of 'Two-Up' involves tossing two coins. Players can bet either on two heads (HH) or two tails (TT). If a head and a tail is thrown (HT or TH), the player continues tossing until either HH or TT results. If $5$ successive tosses result in a $\mathrm{H}$ and $\mathrm{T}$ , all bets loose, and the game is finished. $\newline$ Using your table from Question ( $3$ ), answer the following questions: $\newline$ (a) Find the probability that the game finishes on the first toss. Explain your answer. $\newline$ ( $2$ marks)

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Experimental probability

Full solution

Q. The traditional Australian game of 'Two-Up' involves tossing two coins. Players can bet either on two heads (HH) or two tails (TT). If a head and a tail is thrown (HT or TH), the player continues tossing until either HH or TT results. If

5

successive tosses result in a

\mathrm{H}

and

\mathrm{T}

, all bets loose, and the game is finished.

\newline

Using your table from Question (

3

), answer the following questions:

\newline

(a) Find the probability that the game finishes on the first toss. Explain your answer.

\newline

(

2

marks)

Game of Two-Up: The game of 'Two-Up' finishes on the first toss if either two heads (HH) or two tails (TT) are thrown. Since there are two coins, there are four possible outcomes when they are tossed: HH, HT, TH, and TT. Each outcome is equally likely because the coins are fair. $\newline$ To find the probability of the game finishing on the first toss, we need to calculate the probability of getting either HH or TT. The probability of getting HH on a single toss is $1$ out of $4$ , and the probability of getting TT is also $1$ out of $4$ . $\newline$ The probability of the game finishing on the first toss is the sum of the probabilities of getting HH or TT.
Calculate Probability: Now we calculate the probability of the game finishing on the first toss. $\newline$ $P(\text{Game finishes on first toss}) = P(HH) + P(TT)$ $\newline$ $= \frac{1}{4} + \frac{1}{4}$ $\newline$ $= \frac{2}{4}$ $\newline$ $= \frac{1}{2}$
Calculate Percentage: To express the probability as a percentage, we multiply the fraction by $100$ . $\newline$ $P(\text{Game finishes on first toss})$ in percentage = $(\frac{1}{2}) \times 100\%$ $\newline$ = $50\%$

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