Question

Monshimout is a game from the Cheyenne people and played by women. It could be played by two or more players, and if played by more than two, then the players divided into two equal teams.

Game equipment consisted of five plum stones and a basket made of woven grass or willow twigs. The basket measured 3-4 inches deep, 8 inches across at the top, and almost 1/2 inch thick. The plum stones were left plain on one side, but marked on the opposite side. Three were marked using a pattern similar to markings the women used when painting their face: a cross (used on the bridge of the nose), and side marks (used on cheeks, forehead, and chin). The other two stones were marked with a representation of a bear's foot.

The players sat opposite each other, in two rows if more than one player. Each player has eight sticks which represent the points she must score to win. When a player has won all the sticks belonging to her opponent she has won the game and the stakes wagered. If teams are playing, each member wins or loses according to the winnings or losses of the teammate in control of the basket and stones.

A throw of the stones is done this way. The stones are placed into the basket and the basket is raised slightly and the stones tossed only a few inches and caught in the basket. The basket is then brought down firmly onto the ground so that it strikes the ground with a slight noise. The manner in which the stones land in the basket determine the points scored or lost, as well the control of the throw. A player continues to throw so long as she throws a scoring toss, if she throws a toss with no score the throw passes to her opponent or to the next player. If teams are playing it passes to the thrower's teammate and continues as such until the last teammate throws. If the last member of a team throws a zero score the throw passes to the opposing team.

The scoring is as follows:
5 blanks = 1 (the thrower takes 1 stick)
3 blanks, 2 bears = 1 (thrower takes 1 stick)
2 bears, 2 crosses, 1 blank = 1 (thrower takes 1 stick)
2 blanks, 3 crosses = 3 (thrower takes 3 sticks)
2 bears, 3 crosses = 8 (thrower takes 8 sticks and wins game)

Assuming that each stone has equal chance of landing on either side, compute the following:

The probability of 5 blanks: =  
The probability of 3 blanks, 2 bears: =  
The probability of 2 bears, 2 crosses and 1 blank: =  
The probability of 2 blanks, 3 crosses: =  
The probability of 2 bears, 3 crosses: =  

Consider the probability distribution of possible points X given below:

Xi	0	1	3	8
P(X=Xi)	P(X=0)	P(X=1)	P(X=3)	P(X=8)

Find the following:

P(X=0) =

P(X=1) =

P(X=3) =

P(X=8) =

Answer 1

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