Question

A fair die is rolled 12 times. Consider the following three possible outcomes:(i) 6 5 4 3 2 1 6 5 4 3 2(ii) 1 1 1 1 1 1 1 1 1 1 1(iii) 3 6 2 1 5 4 2 5 1 6 4 3Which of the following is true?A. The three outcomes are equally likely.B. It is absolutely impossible to get sequence (ii).C. (i) is more likely than (ii).D. (iii) is more likely than (i) or (ii).E. Both (C) and (D) are true.

Answer 1

A. The three outcomes are equally likely

Explanation:

Given

`(i)\ 6, 5, 4, 3, 2, 1, 6, 5, 4, 3, 2, 1`

`(ii)\ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1`

`(iii)\ 3, 6, 2, 1, 5, 4, 2, 5, 1, 6, 4, 3`

Required

Which of the options is true

The sample space of a fair die is:

`S = \{1,2,3,4,5,6\}`

And the probability of each (in a single roll) is:

`P(x) = (1)/(6)`

In 12 rolls, the probability would be:

`P(x) = ((1)/(6))^(12)`

What this means that the elements of the sample space have equal probability of showing up.

So, events (i), (ii) and (iii) are equally likely