An ancient Korean drinking game involves a 14-sided die. The players roll the die in turn and must submit to whatever humiliation is written on the up-face: something like "Keep still when tickled on face." Six of the 14 faces are squares. Let's call them A, B, C, D, E, and F for short. The other eight faces are triangles, which we will call 1, 2, 3, 4, 5, 6, 7, and 8. Each of the squares is equally likely. Each of the triangles is also equally likely, but the triangle probability differs from the square probability. The probability of getting a square is 0.64. Give the probability model for the 14 possible outcomes.

To determine the probability model for the 14 possible outcomes, we need to assign probabilities to each individual outcome. We know that there are 6 squares (A, B, C, D, E, F) and 8 triangles (1, 2, 3, 4, 5, 6, 7, 8). We are also given that the probability of getting a square is 0.64.

Let's denote the probability of getting a square as P(S) and the probability of getting a triangle as P(T). Since we have 14 possible outcomes (6 squares and 8 triangles), the total probability should add up to 1.

We are given that P(S) = 0.64. To find P(T), we can subtract P(S) from 1 because the sum of the probabilities of all outcomes must equal 1.

1 - P(S) = 1 - 0.64 = 0.36

So, P(T) = 0.36.

Now we can assign probabilities to each of the 14 possible outcomes:

P(A) = P(B) = P(C) = P(D) = P(E) = P(F) = P(S) = 0.64

P(1) = P(2) = P(3) = P(4) = P(5) = P(6) = P(7) = P(8) = P(T) = 0.36

The probability model for the 14 possible outcomes is as follows:

P(A) = P(B) = P(C) = P(D) = P(E) = P(F) = P(S) = 0.64

P(1) = P(2) = P(3) = P(4) = P(5) = P(6) = P(7) = P(8) = P(T) = 0.36