# Question 1 : You roll a pair of dice. a) What is the probability of rolling a total of 11? b) You roll the dice twice. What is the probability of getting at least one total of 11? c) You now roll the dice 24 times. What is the probability of rolling at least one total of 11? d) Got the ides? OK then, if you roll the dice n times, what is the probability of rolling at least one total of 11? Question 2 : A gambler made three 6-sided dice. The red die had the numbers 2,4 and 9 each appear twice on its faces. The blue die had the numbers 3,5 and 7 eachappear twice on its faces. The yellow die had the numbers 1,6 and 8 each appear twice on its faces. The total of faces of each dice is the same. In the Gambler's Game his opponent chooses any die first and then rolls it. The gambler then chooses a die and rolls it. He is confident he can always choose a die that would give him a better chance of obtaining a higher score. Explain why the gambler is correct to be confident and provide calculations to support your explanation. Describe the variation on the gambler's game that would give him even a better chance of winning. Create another set of three dice that would serve the gambler equally as well, but this time each face on a single die must be a different number and no number can be used more than once. Again use calculations to explain why your new dice also work. Question 3 : You want to throw a patry for 10 men and 10 women but your backyard can only hold 10 people. So you decide to throw a series of parties so that every man and woman will have the opportunity to meet at one of your parties. Unfortunately you have limited funds so you want to make sure that you hold the minimum nomber of parties for everyone to meet. You talk to your neighbour about the parties and she says you should not need any more than four parties. Show that she is correct.

**Question 1****:**

You roll a pair of dice.

a) What is the probability of rolling a total of 11?

b) You roll the dice twice. What is the probability of getting at least one total of 11?

c) You now roll the dice 24 times. What is the probability of rolling at least one total of 11?

d) Got the ides? OK then, if you roll the dice n times, what is the probability of rolling at least one total of 11?

**Question 2****:**

A gambler made three 6-sided dice.

The red die had the numbers 2,4 and 9 each appear twice on its faces.

The blue die had the numbers 3,5 and 7 eachappear twice on its faces.

The yellow die had the numbers 1,6 and 8 each appear twice on its faces.

- The total of faces of each dice is the same. In the Gambler's Game his opponent chooses any die first and then rolls it. The gambler then chooses a die and rolls it. He is confident he can always choose a die that would give him a better chance of obtaining a higher score. Explain why the gambler is correct to be confident and provide calculations to support your explanation.
- Describe the variation on the gambler's game that would give him even a better chance of winning.
- Create another set of three dice that would serve the gambler equally as well, but this time each face on a single die must be a different number and no number can be used more than once. Again use calculations to explain why your new dice also work.

**Question 3****:**

You want to throw a patry for 10 men and 10 women but your backyard can only hold 10 people. So you decide to throw a series of parties so that every man and woman will have the opportunity to meet at one of your parties. Unfortunately you have limited funds so you want to make sure that you hold the minimum nomber of parties for everyone to meet. You talk to your neighbour about the parties and she says you should not need any more than four parties. Show that she is correct.

## 1 Answers

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