You place a 1-dollar bet on the number 17 at Las Vegas, and yourf frined places

Question

You place a 1-dollar bet on the number 17 at Las Vegas, and yourf frined places a 1-dollar bet on black. Let X be your winnings and Y be her winnings. Compare E(X), E(Y), and V(X), V(Y). What do these computations tell you about the nature of your winnings if you and your fined make a sequence of bets, with you betting each time on a number and your friend betting on a color? You place a 1-dollar bet on the number 17 at Las Vegas, and yourf frined places a 1-dollar bet on black. Let X be your winnings and Y be her winnings. Compare E(X), E(Y), and V(X), V(Y). What do these computations tell you about the nature of your winnings if you and your fined make a sequence of bets, with you betting each time on a number and your friend betting on a color?

Explanation / Answer

There are 18 black slots, 18 red slots and two green slots (0 and 00) on a US roulette wheel...so the chances of getting black(red)=18/38

E(Y)=18/38*1$ + 20/38*( -1$) =-2/38 $= -.052$

bets made on the chart of the various numbers 1 to 36 and zero. Just put a chip down in the middle of the square with the number you select. If it comes up, it pays 35-to-1. It is called a straight up bet.

So chance of getting selected number=1/38

E(X)= 1/38* 35$ + 37/38* (-1$)= -2/38$= -.052$

So v(X)= {1-(1/19)^2}=.997

V(Y)={35^2*(1/38) - (1/19)^2*1}=32.23

So the expectations are same i.e, both will lose same amount of money if they play for 38 times....but variances are different.... The girl who is betting on colour is little chance to gain and lose but the boy on number has huge deviation....

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