Chapter 6 - EXPECTED VALUE AND VARIANCE

Problem 4

In Las Vegas the roulette wheel has a 0 and a 00 and then the numbers 1 to 36 marked on equal slots; the wheel is spun and a ball stops randomly in one slot. When a player bets 1 dollar on a number, he receives 36 dollars if the ball stops on this number, for a net gain of 35 dollars; otherwise, he loses his dollar bet. Find the expected value for his winnings.

From the information:

Total number on Roulette wheel = 38 (including 0 and 00)

Net gain when he win = $ 35

Probability of Win = \(\frac {1}{38}\)

Probability of Loss = \(\frac {37}{38}\)

Therefore,

ProbWin <- 1/38
ProbWin
## [1] 0.02631579
ProbLoss <- 37/38
ProbLoss
## [1] 0.9736842
# Expected Value

Exp <- (-1*ProbLoss)+(35*ProbWin)
Exp
## [1] -0.05263158

The expected value for his winnings is - 0.05263