The game of roulette involves spinning a wheel with 38 slots: 18 black, 18 red a

Question

The game of roulette involves spinning a wheel with 38 slots: 18 black, 18 red and 2 green. A ball
is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of
capturing the ball. Gamblers can place bets on red or black. If the ball lands on green, the
gambler loses. If the ball lands on their color, they double their money. If it lands on another
color, they lose their money. Suppose you bet $2 on red. What’s the expected value and
standard deviation of your winnings?

Explanation / Answer

probabilty of losing 1st game =P(X=-2)=20/38=0.5263

probabilty of winning 1st game and losing second =P(X=-2)=(18/38)*(20/38)=0.2493

probabilty of winning 1st game and winning second =P(X=4)=(18/38)*(18/38)=0.2244

from above:

hence expected winning =-0.65

and std deviation =(6.6925-(-0.6537)2)1/2 =2.50

x P(x) xP(x) x^2P(X) -2 0.5263 -1.0526 2.1053 -2 0.2493 -0.4986 0.9972 4 0.2244 0.8975 3.5900 total 1 -0.6537 6.6925

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