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please explain the following simple probability question!?
In the game of roulette, if I bet on dollar on red,I win a dollar with
probability 18/38.
My total win, W, in 2 plays is a random variable. Write down its
probability distribution?
please also explain how the game works?:)
thanks
also,
Expected value of W =
?
Standard. deviation of W = ?
1 Answer
- Christopher SLv 41 decade agoFavorite Answer
Roulette is a game which has 38 numbers on a wheel 1 to 36 and 0 and 00 - American Roulette Wheel. The zeros are in a green color and the numbers 1 to 36 are either colored black or red. So there are 18 red numbers and 18 black numbers. If you land on a zero - you lose if you are just betting on red or black. so in two spins you can have
W,W
W,L
L,W
L,L
You have 4 different combinations that you can have in 2 spins
1 win win combination 2 win lose combinations and 1 lose lose combination.
so n=2 p=18/38 q=20/28 p=wins q=losses X= no of wins/loses
X Pr(X) probability distribution
0 (1)(18/38^0)(20/38^2)= (1)(1)(0.277)=0.277
1 (2)(18/38^1)(20/38^1)= (2)(18/38)(20/38)=0.499
2 (1)(18/38^2)(20/38^0)= (1)(0.22437)(1)=0.224
So the probability of zero wins is 0.277
The probability having a win and a lose in the 2 spins is 0.499 and 2 wins is 0.224. There is your probability distribution.