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The game of American roulette involves spinning a wheel with 38 slots: 18 red, 18 black, 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 their color, they double their money. If it lands on another color, they lose their money. Suppose you bet $1 on red.(a) What's the expected value of your winnings?(b) What's the standard deviation of your winnings?

Respuesta :

Answer:

a)[tex] - \frac{1}{19}[/tex]

b) SD(x) =  0.9986

Step-by-step explanation:

Given data:

Number of slots 38

slots for red ball 18

slots for black = 18

slots for green 2

outcomes       Red      Black or Green

Profit                  1                 -1

P(X)                   18/38       20/38

Expected value of wining,  

[tex]E(x) = 1. \frac{18}{38} + (-1) \frac{20}{38} = - \frac{2}{38} = - \frac{1}{19}[/tex]

B) Standard deviation of winning SD(x)

[tex]SD(x) = \sqrt{(1- (-\frac{1}{19})^2 .\frac{18}{38} + (1- (-\frac{1}{19})^2 .\frac{20}{38}}[/tex]

[tex]SD(x) = \sqrt{\frac{360}{361}[/tex]

SD(x) =  0.9986

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