Question:
A die has its six faces marked 0, 1, 1, 1, 6, 6. Two such dice are thrown together and the total score is recorded.
(i) How many different scores are possible?
(ii) What is the probability of getting a total of 7?
Solution:
Given, a die has its six faces marked {0,1,1,1,6, 6}
Total sample space, n(S) = 62 = 36
(i) The different score which are possible are 6 scores e., 0,1,2,6,7 and12.
(ii) Let E = Event of getting a sum 7
$=\{(1,6),(1,6),(1,6),(1,6),(1,6),(1,6),(6,1),(6,1),(6,1),(6,1),(6,1),(6,1)$
$\therefore \quad n(E)=12$
$\therefore \quad P(E)=\frac{n(E)}{n(S)}=\frac{12}{36}=\frac{1}{3}$