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 $7$.

Answer 1

Different scores that are possible as a combination of both dices are thrown -

(0,0) = 0

(0,1) = 1

(0,6) = 6

(1,1) = 2

(1,6) = 7

(6,6) = 12

To get a score of 7, one dice must show 1 and one dice must show 6.

Probability of dice getting 1 = 3/6 = 1/2.

Probability of dice getting 6 = 2/6 = 1/3.

Thus probability of getting score 7 is =

1/2 * 1/3 + 1/2*1/3 = 1/3.