1.2.8 Let E be the experiment consisting of tossing a die twice. Let S be the sample space with sample points (2, j ) , i, j = 1 , 2 , . . .6, with i and j being the numbers of dots that appear in the first and second toss, respectively.

(i) Let S’ be the sample space for the experiment E consisting of all possible sums i + j so that S’ = {2,3, . . . , 12). Which of the following events can be defined as subsets of S but not of S‘?

A1 = One face odd, the other even.

A2 = Both faces even.

A3 = Faces different.

A4 = Result on the first toss less than the result on the second.

A5 = Product greater than 10.

As = Product greater than 30.

(ii) Let S” be the sample space for the experiment & consisting of all possible absolute values of the difference Ii - j l so that S” = { 0 , 1 , 2 , 3 , 4 , 5 } . Which of the following events can be defined as subsets of S but not of S”?

B1 = One face shows twice as many dots as the other, B2 = Faces the same, B3 = One face shows six times as many dots as the other, B4 = One face odd, the other even, B5 = The ratio of the numbers of dots on the faces is different from 1.