A roulette wheel has 38 slots, numbered 0, 00, and 1 to 36. The slots 0 and 00 are colored green, 18 of the others are red, and 18 are black. The dealers spin the wheel and at the same time rolls a small ball along the wheel along the wheel in the opposite direction. The wheel is carefully balanced so that the ball is equally likely to land in any slot when the wheel slows. Gamblers can bet on various combinations of numbers and colors. There is a player who will bed on RED every time he plays, and he plays 10 games in total, with same amount of bet on each game. (
010=1,110=10,210=45,310=120,410=210 ,510=252,610=210,710=120,810=45,910 =10,1010=1
C
10
0
=
1
,
C
10
1
=
10
,
C
10
2
=
45
,
C
10
3
=
120
,
C
10
4
=
210
,
C
10
5
=
252
,
C
10
6
=
210
,
C
10
7
=
120
,
C
10
8
=
45
,
C
10
9
=
10
,
C
10
10
=
1
010=1,110=10,210=45,310=120,410=210 ,510=252,610=210,710=120,810=45,910 =10,1010=1
C
10
0
=
1
,
C
10
1
=
10
,
C
10
2
=
45
,
C
10
3
=
120
,
C
10
4
=
210
,
C
10
5
=
252
,
C
10
6
=
210
,
C
10
7
=
120
,
C
10
8
=
45
,
C
10
9
=
10
,
C
10
10
=
1

C
10 0 = 1 , C 10 1 = 10 , C 10 2 = 45 , C 10 3 = 120 , C 10 4 = 210 , C 10 5 = 252 , C 10 6 = 210 , C 10 7 = 120 , C 10 8 = 45 , C 10 9 = 10 , C 10 10 = 1)

(1) (2pts) Define variable X = Number of games the player wins out of 10 games he plays. What is the distribution of variable X? (Please indicate both distribution name and parameters).

(2) (1pt) What is the sample space of the variable X?

(3) (4pts) What is the probability that he WINS any amount of money? (No points without necessary steps).

(4) (2pts) What is the probability that he BREAK EVEN? (No points without necessary steps).

(5) (4pts) What is the probability that he LOSES any amount of money?(No points without necessary steps).