European: There is one additional pocket colored green and labeled 0 (for a tota

Question

European: There is one additional pocket colored green and labeled 0 (for a total of
18+18+1=37 pockets). An example of this wheel is pictured below on the left.
American: There are two additional pockets colored green labeled 0 and 00 (for a total
of 18+18+2=38 pockets). An example of this wheel is pictured below on the right

(a) [easy] What is the probability of the ball landing in a black pocket? Calculate for both
European and American roulette.
(b) [easy] What is the probability of the ball landing in a green pocket? Calculate for both
European and American roulette.
(c) [easy] What is the probability you see RRBBBRGRBB in 10 spins in Las Vegas?
(d) [easy] In the 18 red pockets there are 9 even numbered pockets and 9 odd numbered
pockets. What is the probability of getting a pocket wihich is both Red and Odd in
Las Vegas?
(e) [easy] What is the probability you see a spin that is both Red and Green in Las Vegas?
(f) [easy] What is the probability you see a spin that is Red or Green in Amsterdam?
(g) [easy] In Las Vegas, you play the game 10 times and always bet on black. What is the
probability you win all 10 times?
(h) [harder] In Las Vegas, you see BBBBBBBBBB. Conditional on seeing this event, what
is the probability the next spin is R?
(i) [harder] In Las Vegas, what is the probability of BBBBBBBBBBR? This is the same
situation as in the previous question, but framed dierently (in order to confuse you).
(j) [dicult] In Las Vegas, you play the game 10 times and always bet on black. What is
the probability you win at least once?

Explanation / Answer

a) European: P(black) = 18/37 = 0.4865
American: P(Black) = 18/38 = 9/19 = 0.4737

b) European: P(Green) = 1/37 = 0.027027
American: P(Green) = 2/38 = 1/19 = 0.05263

c) P(R) = P(B) = 18/38
P(RRBBBRGRBB) = (18/38)^10 = 0.000568708

d) There are 9 red and odd pockets out of 38
P(red and odd) = 9/38 = 0.2368

e) P(red and green) = 0(It cannot happen)

f) P(Red or Green in Europe) = 19/37 = 0.5135

g) P(10 times black) = (18/38)^10 = 0.000568708

h) P(R after BBBBBBBBBB) = 18/38 = 0.4737(It is not dependent on previous spins)

i) P(BBBBBBBBBBR) = (18/38)^11 = 0.0002694

j) P(win atleast once) = 1 - P(win none) = 1 - (20/38)^10 = 1 - 0.001631 = 0.9984

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