The roulette wheel has 38 compartments of which 18 are red 1

The roulette wheel has 38 compartments, of which 18 are red, 18 are black, and two are green. As the wheel is spun, a small metal ball bounces around until it settles in one of the compartments. If you bet 1 dollar on red at roulette. Your dollar will be returned to you along with one more dollar if red comes up. otherwise you will lose that dollar.

(a) Write down the probability distribution table for your return.

(b) Find your expected return.

Solution

a)

Here, the probability that you win is 18/38, while the probability of losing is 20/38.

Thus,

P(x) = 0.526315789, x = -1
0.473684211, x = 1 [ANSWER]

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Consider the table:      
      
x   P(x) x P(x)
-1   0.526315789   -0.526315789
1   0.473684211   0.473684211
      
Totals -0.052631579
=E(x)
      
Thus,      
      
E(x) =    -0.052631579 [ANSWER]