Six faces of a die are numbered 1,2,2,3,3,6. The die is rolled twice. The total score in two rolls is noted. Complete the following tabel which gives a few values of the total score on the two rolls. What is the probability that the total score is (i) even (ii) 6 (iii) at least 6?

Explanation

The completed table is given below:

Here `n(S)=36`
(i) Let A be the event that the total score is even.
Then `A={2,4,4,4, 8,4,4,48,4,6,6,5,6,6,8,8,12}`
`:.n(A)=18`
`:.P(A)=(n(A))/(n(S)) P(A)=18/36=1/2`
(ii) Let B be the event that the total score is 6.
Then `B={6,6,6,6}:.n(B)=4`
`:.P(B)=(n(B))/(n(S)):.P(B)=4/36=1/9`
(iii) Let C be the event that the total score is at least 6.
Then `C={7,8,8,6,6,9,6,6,9,7,8,8,9,9,12}`
`:.n(C)=15`
`:.P(C)=(n(C))/(n(S))impliesP(C)=15/36=5/12`
An. (i) `1/2` (ii) `1/9` (iii) `5/12`