Probability, SM-Bank 061

Chusi uses this net to make a dice.

Chusi rolls the dice once. What is the chance that Chusi will roll a 2? (1 mark)
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Chusi makes up a game and to win the game you must roll a number larger than 2.
What is the chance that Chusi will win the game on her next roll? (1 mark)

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If Chusi rolls the dice 108 times, how many times could she expect to win the game? (1 mark)
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Show Answers Only

a. \(\dfrac{1}{3}\)

b. \(\dfrac{1}{6}\)

c. \(18\ \text{times}\)

Show Worked Solution

a.	\(P(2)\)	\(=\dfrac{\text{number of 2’s}}{\text{total possibilities}}\)
		\(=\dfrac{2}{6}\)
		\(=\dfrac{1}{3}\)

b.	\(P\text{(number>2)}\)	\(=\dfrac{\text{number of 3’s}}{\text{total possibilities}}\)
		\(=\dfrac{1}{6}\)

\(\therefore\ \text{Chusi’s chance of winning on the next roll is }\dfrac{1}{6}.\)

c.	\(\text{Expected wins}\)	\(=\text{number of rolls}\times \text{probability of winning}\)
		\(=108\times \dfrac{1}{6}\)
		\(=18\)

\(\therefore\ \text{Chusi could expect to win 18 times with 108 rolls.}\)