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

A) SEE PROBABILITY IS EITHER WE WILL WIN AUR LOSE MONEY

SO P(0) = 37/38 ( BECAUSE WE WILL LOSE IF ANYTHINGS ELSE COMES OTHER THAN ON WHICH WE BET)

P(1)= 1/38

B) EXPECTED VALUE = 0P(0) +1P(1)

= 0*37/38+1*1/38= 1/38

C)SINCE PROBILITY OF WINNING IS 1/38 THAT = 2.6% SO BETTING ON RED 100 TIMES AND ACCORDING TO WINNING PROBABILITY WE WILL WIN 2.6$

D) NO ITS NOT A PROFITABLE GAME BECAUSE THE WINNING PROBABILITY IS VERY LESS THAN THE LOSING PROBABILITY