A roulette wheel contains 38 numbers 18 are red 18 are black

A roulette wheel contains 38 numbers: 18 are red, 18 are black, and 2 are green. When the roulette is spun, the ball is equally likely to land on any of the 38 numbers. You bet on $1 on red, which has a payout of $1. Let X be the amount you win on your $1 bet.

a) Make a table showing the probability distribution of the random variable X.

b) Find the expected value of the random variable X.

c) Approximately how much would you expect to lose if you bet $1 on red 100 times?

d) Is roulette a profitable game? Explain why or why not.

Solution

the possible vlues of x are won $1 and lost $1

X,,,,,,,,,,,,,,,,,,1..................-1

P(X)..............18/38...........20/38

b)

expected value of X

= 1 * 18/38 + -1 * 20/38

= -1/19 = -0.05

c)

expected loss = 0.05 * 100 * $1= $5

d)

if the payout is same as bet , it not profitable by any chance

if the payout is high , there is a chance that it is profitable

although odds favour loosing