DIE DIE MUST ...

Fair 6-sided dice are used in the questions.

(1) Throwing 1 die, what is the probability of getting a 6?


(2) Throwing 2 dice, what is the probability of getting a sum of 6?


(3) Throwing 3 dice, a sum of 10 is more likely or a sum of 9?


Do NOT peep the answers before you attempt the questions!

No... No... No... PEEPS YET...

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Answers:
(1) 1/6
(2) Tabulate the results, you can see there are 5 times of sum 6 out of the total 36 outcomes. So it is 5/36.
(3) 9: (621) (531) (522) (441) (432) (333)
10: (631) (622) (541) (532) (442) (432)
Do they have the same chance? Not really.

Let's see. For example, (6 2 1) there are 6 different ccombinations 126, 162, 216, 261, 612, 621.
If we do that, we find that there are 27 ways of getting 10 and 25 ways of getting 9. Hence, 10 is more likely to appear.