A fair die is rolled 12 times. Consider the following three possible outcomes:

Question

(i) 5 2 6 3 2 1 4 1 6 5 3 4
(ii) 1 1 2 2 3 3 4 4 5 5 6 6
(iii) 6 6 6 6 6 6 6 6 6 6 6 6
Which of the following is true?


(i) is more likely than (ii) or (iii).

(ii) is more likely than (iii).

The three outcomes are equally likely.

It is absolutely impossible to get sequence (iii).

Both (A) and (B) are true.

Answer 1

iii) is extremely unlikely but not impossible.

i) is certainly possible and in fact every # from 1 thru 6 occurs twice. you do not say if the order of presentation of these numbers is the order in which they occurred.

(ii) is certainly possible but the likelihood of outcomes appearing in this particular order is fairly low, because random order would be expected.

 

It makes no sense to entertain the question   "Both (A) and (B) are true"  -- simply because there is no A or B.  Besides, a list of outcomes is an observed fact, and it's not a question of truth.