Consider a game with three dice, namely, A, B and C. Each die, when rolled, generates a number between 1 and 6 (inclusive) independently and uniformly at random. In each play, the three dice are rolled, then a monetary return is computed according to the values for dice A, B and C, using the following algorithm. ThreeDice(A, B, C) { money = -9; if (A == B and B == C) { money = money + 81; } else if (A == B or B == C or C == A) { money = money + 21; } return money; } Analyze this game by answering the following questions: (a) What is the largest possible return value of ThreeDice? (b) What is the probability of ThreeDice returning the largest possible value? Choose one from below. A. 1/18 B. 1/3 C. 1/216 D. 1/2 E. 1/6 F. none of these is correct G. 1/36 H. 1/12 (c) What is the smallest possible return value of ThreeDice?
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Consider a game with three dice, namely, A, B and C. Each die, when rolled, generates a number between 1 and 6 (inclusive) independently and uniformly at random. In each play, the three dice are rolled, then a monetary return is computed according to the values for dice A, B and C, using the following
ThreeDice(A, B, C) { money = -9; if (A == B and B == C) { money = money + 81; } else if (A == B or B == C or C == A) { money = money + 21; } return money; }
Analyze this game by answering the following questions:
(a) What is the largest possible return value of ThreeDice?
(b) What is the probability of ThreeDice returning the largest possible value? Choose one from below.
A. 1/18
B. 1/3
C. 1/216
D. 1/2
E. 1/6
F. none of these is correct
G. 1/36
H. 1/12
(c) What is the smallest possible return value of ThreeDice?
(d) What is the probability of ThreeDice returning the smallest possible value? Choose one from below.
A. 5/54
B. 1/18
C. 5/9
D. 4/9
E. 1/36
F. None of these is correct.
G. 2/9
(e) What is the expected return value of ThreeDice? Choose one from below.
A. 3
B. 2
C. None of these is correct.
D. 1
E. 5
F. 6
G. 8
H. 4
I. 7
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