Question

There are three dices, a person tosses 3 dices every time. If the number of three dices is in 3-10, he loses the game; If the number of three dices is in 11-18, he wins the game. Find out the chances (rate) of winning the prize.

Answer 1

There are three dices, and the person tosses 3 of them simultaneously.

The total sample, S= {{1,1,1},{1,1,2}....{6,6,5},{6,6,6}}, n(S)= 6³

Now, Chance of winning the prize for the person \

= Probability that the sum of all the numbers on the face of the die add between 11-18

= Probability that the sum of the all the numbers on the face of the die > 10

= 1 - Probability that the sum of the all the numbers on the face of the die < 11

The favourable outcomes can be-

{{1,1,1},{1,1,2},{1,1,3},{1,1,4},{1,1,5},{1,1,6},{1,2,1},{1,2,2},{1,2,3},{1,2,4},{1,2,5},{1,3,1},{1,3,2},{1,3,3},{1,3,4}{1,3,5},{1,3,6},

{1,4,1},{1,4,2},{1,4,3},{1,4,4},{1,4,5},{1,5,1},{1,5,2},{1,5,3},{1,5,4},{1,6,1},{1,6,2},{1,6,3}

{2,1,1},{2,1,2},{2,1,3},{2,1,4},{2,1,5},{2,1,6},{2,2,1},{2,2,2},{2,2,3},{2,2,4},{2,2,5},{2,3,1},{2,3,2},{2,3,3},{2,3,4}{2,3,5},

{2,4,1},{2,4,2},{2,4,3},{2,4,4},{2,5,1},{2,5,2},{2,5,3},{2,6,1},{2,6,2}

{3,1,1},{3,1,2},{3,1,3},{3,1,4},{3,1,5},{3,1,6},{3,2,1},{3,2,2},{3,2,3},{3,2,4},{3,2,5},{3,3,1},{3,3,2},{3,3,3},{3,3,4},

{3,4,1},{3,4,2},{3,4,3},{3,5,1},{3,5,2},{3,6,1},

{4,1,1},{4,1,2},{4,1,3},{4,1,4},{4,1,5},{4,2,1},{4,2,2},{4,2,3},{4,2,4},{4,3,1},{4,3,2},{4,3,3},

{4,4,1},{4,4,2},{4,5,1}

{5,1,1},{5,1,2},{5,1,3},{5,1,4},{5,2,1},{5,2,2},{5,2,3},{5,3,1},{5,3,2}, {5,4,1},

{6,1,1},{6,1,2},{6,1,3},{6,2,1},{6,2,2},{6,3,1}}

n(favourable outcomes) = 108

Probability of winning = 1 - (108/216) = 0.5