An ancient Korean drinking game involves a 14sided die The p

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 0.66. Give the probability model for the 14 possible outcomes. (Round your answers to three decimal places.)

Solution

WE HAVE SQUARE AS A,B,C,D,E

TRIANGLES AS 1,2,3,4,5,6,7,8

TOTAL THERE ARE 14 SIDES

GIVEN THAT THE PROBABILITY OF GETTING SQUARE = 0.66

HENCE PROBABILITY OF GETTING TRIANGLE = 1-0.66 = 0.34

SO PROBABILITY OF GETTING A = 1/6*0.66 = 0.11( AS A IS SQUARE AND THR ARE TOTAL 6 SQUARE, THEREFORE PROBABILITY OF SINGLE SQUARE = 0.11)

SIMILARLY PROBABILITY FOR ALL SQUARE = 0.11

HENCE FOR A,B,C,D,E,F PROBABILITY = 0.11 EACH

SIMIALRLY PROBABILITY OF GETTING 1 = 0.34*(1/8) = 0.0425 ( AS PROBABILITY OF GETTING TRAINGALE = 0.34 HENCE PROBABILITY OF GETTING SINGLE = 1/8*0.34)

SIMILARLY FOR ALL 1,2,3,4,5,6,7,8 THE PROBABILITY WILL BE 0.0425 EACH