Question

Find the expected value for the bettor of $50 on red and $20 on black for one play of roulette. Round to the fourth as needed. Reference class notes for information on the Roulette wheel.

Answer 1

In a roulette there are 18 reds, 18 blacks and 2 greens, so Probability of getting a red on a single spin= 18/38, probability of getting a black= 18/38

Now, if red comes, 50 becomes 100 with probability 18/38 or -50(losing 50) with probability 20/38

So expected value of 50= 100*18/38 -50*20/38 = 400/19

Similarly 20 becomes 40 with probability 18/38 or -20 with probability 20/38

So expected value of 20= 40*18/38 -20*20/38 = 160/19

So total required expected value = 400/19 +160/19 = 29.474