answer 0078704 Dont know how to get this answer please help

answer: ?0.078704

Don\'t know how to get this answer, please help.

The game of sic bo is played by rolling three dice. If the player bets on number I {1,2,3,4,5,6} ,he paid k to 1 if number I appears k times(k=1,2,3),and he loses his bet if number I does not appear. Let X be the number of time that number I appears, and let Y be the player\'s profit from a one- unit best .Observe that X is binomial (3,1/6)and Y =X-1{X=0} Use this observation to find E(Y).

Solution

Y=X-1

E(Y)= E(X-1) = E(X)-1 = n*p-1= 3*(1/6)-1 = -0.5

Another way

E(Y) = sum of ( Y*P(Y))= -0.5

X	P(X)	X*P(X)	Y	Y*p(Y)
0	0.578704	0	-1.000	-0.5787
1	0.347222	0.347222	0	0
2	0.069444	0.138889	1	0.069444
3	0.00463	0.013889	2	0.009259
	Total	0.5000		-0.500