A triangular die is a four-sided die, each side possessing either a number 1, 2,

Question

A triangular die is a four-sided die, each side possessing either a number 1, 2, 3, or 4. Two such die are tossed simultaneously and the bottom faces - the face that each die lands on - is observed. Consider the following events: A the bottom-most faces sum to six B each bottom-most face shows an even number C both bottom-most faces show the same number, referred to as doubles Part (a) What is the probability that the bottom-most faces do not sum to six? Part (b) Find P(AB) Part (c) Find P(AcCc) Part (d) Find P(ABC)

Explanation / Answer

When two triangular dice are rolled, there are 4^2 = 16 outcomes are possible.

A: A the bottom-most faces sum to six. (2,4) (3,3) (4,2)

P(A) = 3/16 = 0.1875

B: each bottom-most face shows an even number. (2,2) (4,4)

P(B) = 2/16 = 0.125

C: both bottom-most faces show the same number. (1,1) (2,2) (3,3) (4,4)

P(C) = 4/16 = 0.25

(a)

the probability that the bottom-most faces do not sum to six = 1 - P(B) = 1 - 0.125 = 0.875

(b)

(A U B) = {(2,4) (3,3) (4,2) (2,2) (4,4))

P(A U B) = 5/16 = 0.3125

(c)

P(A' and C') = P(A U C)' = 1 - P(A U C)

(A U C) = {(2,4) (3,3) (4,2) (1,1) (2,2) (4,4)}

P(A U C) = 6/16 = 0.375

P(A' and C') = P(A U C)' = 1 - P(A U C) = 1 - 0.375 = 0.625

(d)

(A and B and C) = {}

P(A and B and C) = 0

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