Probability

a) The first dice can be one of (1, 3, 5), so the prob. is 3/6.The second can only be other 2 numbers, so the prob. is 2/6.The third one is the rest number, so the prob. is 1/6.So, the prob. of getting these three numbers is :(3/6) x (2/6) x (1/6)= 1/36
b) Same as (a), the prob. is also (3/6) x (2/6) x (1/6).So the prob. is also 1/36.

c) Of course, these 2 questions share the same meaning.

> a) P(1,3,5)=(1/6)^3 *6

Actually it means there.

(a) (1/6) x (1/6) x (1/6) = 1/216
(b) (1/6) x (1/6) x (1/6) x 6 = 1/36
Explanation: 6 permutations are possible: 1,3,5; 1,5,3; 3,1,5; 3,5,1; 5,1,3; 5,3,1
(c) No. Different possible permutations exist and hence has to be counted in (b) but not (a)

2014-02-19 21:14:38 補充：
grammatical mistake: ... and hence 'have' to be counted ...

2014-03-06 02:35:31 補充：
Actually my mindset is that the first question is asking the probability of having the result (1,3,5) IN ORDER. So if the order is important, we should use 3c3 instead of 3p3 as the nominator? True or false?

2014-03-06 02:38:21 補充：
And I actually understood why most of you took 1/36 as the answer, with 6 possible permutations in part (a). So I guess we're both correct, our answers are different only because the question is not clear about the importance of order.

(a) Total possible outcomes = 6³ = 216
　 Number of favourable outcomes = 3! = 6
　 The req. prob. = 6/216 = 1/36

2014-02-19 20:08:45 補充：
(b) In the first roll, you have three favourable choices; in the second roll, you have two favourable choices; in the last roll, you just have one favourable choice.
The req. prob. = (3/6) (2/6) (1/6) = 1/36

2014-02-19 20:09:33 補充：
(a) assumes three dice are unbiased and independent.
(b) assumes the dice is unbiased and all throws are independent.

2014-02-19 20:10:47 補充：
(c) Do the two questions share the same meaning?

You can say yes, you can say no.

This answer is hard to answer.
I can argue for the "yes" answer.
I can also argue for the "no" answer.

Therefore, I do not answer you at all.

2014-02-20 00:10:26 補充：
不好意思，Nathan，我相信 (a) 部的答案都是 1/36。

請再想想。　加油！