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?
Accepted Solution
A:
Answer:a)[tex] - \frac{1}{19}[/tex]b) SD(x) = 0.9986Step-by-step explanation:Given data:Number of slots 38slots for red ball 18slots for black = 18slots for green 2outcomes Red Black or GreenProfit 1 -1 P(X) 18/38 20/38Expected 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