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Im unsure on my answers and would like them checked if possible as well as some help with the representation of the sample space.

1, Two six sided dice are thrown and the results recorded. on a suitable diagram representing the sample space, identify the following events:

(a) At least one result is a six;

(b) Both results are the same;

(c) The results total at least nine;

(d) One result is twice the other.

2, If, in the previous question, the dice are fair, find the probabilities of the four events.

Although im not sure what diagram to use to represent the data i am thinking this so far:

(a) Because there are 2 dice, the total possible outcomes are $6^2$ because there are 2 dice with 6 possible outcomes on each die. This gives us 36 possible outcomes, and of these 36, 11 can have the event of at least one 6 so the probability is $\frac{11}{36}$

(b) Again because there are 2 dice, there are 36 possible outcomes and of these 36 outcomes there are only 6 possible outcomes giving a probability of $\frac{6}{36}$ or $\frac16$

(c) 36 possible outcomes, and there are only 10 ways giving a probability of $\frac{10}{36}$

(d) 36 possible outcomes, and there are only 6 possible outcomes, giving a probability of $\frac6{36}$ or $\frac16$

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Edited as wrongly copied, sorry. – Matt Nov 15 '12 at 20:06
As for how you would diagram the space, the space consists of pairs of numbers (the result from die one and the result from die two.) What is a quick way to "show" the set of all such pairs? (For example, how would you represent the multiplication table of all $x\times y$ where $x=1,2,..,6$ and $y=1,2,...,6$? Would you list:$$1\times 1=1\\1\times 2=2\\\dots$$ or can you think of a better way to "list" these formulas? – Thomas Andrews Nov 15 '12 at 20:13
The actual calculations of the probabilities looks right. – Thomas Andrews Nov 15 '12 at 20:19
up vote 1 down vote accepted

You could use a grid and highlight the cases you want such as for (b)

enter image description here

Your answers to (2) can then be checked, but they seem to be correct.

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