Roulette is a casino game that involves players betting on where a ball will land on a spinning wheel. An American roulette wheel has
38
3838 numbered slots — half of the slots from
1
11 to
36
3636 are red and the other half are black. Slots
0
00 and
00
0000 are both green.
Suppose that a player bets
$
1
$1dollar sign, 1 on the color red. If the ball lands in a red slot, the player gets their initial
$
1
$1dollar sign, 1 back plus a payout of
$
1
$1dollar sign, 1. If the ball doesn't land in a red slot, they lose their
$
1
$1dollar sign, 1 bet. Let
X
=
X=X, equals the player's net gain from a
$
1
$1dollar sign, 1 bet on a the color red. Here is the probability distribution of
X
XX: