Question

When playing roulette at a​ casino, a gambler is trying to decide whether to bet ​$20 on the number 34 or to bet ​$20 that the outcome is any one of the three possibilities 00 comma 0 comma or 1 . The gambler knows that the expected value of the ​$20 bet for a single number is negative $ 1.05 . For the ​$20 bet that the outcome is 00 comma 0 comma or 1 ​, there is a probability of StartFraction 3 Over 38 EndFraction of making a net profit of ​$80 and a StartFraction 35 Over 38 EndFraction probability of losing ​$20 .a. Find the expected value for the ​$20 bet that the outcome is 00 comma 0 comma or 1 .b. Which bet is​ better: a ​$20 bet on the number 34 or a ​$20 bet that the outcome is any one of the numbers 00 comma 0 comma or 1 ​? ​Why?

Answer 1

Answer:

a. -$12.11

b. Bet on number 34 is better. Has the highest expected value  of the two.

Step-by-step explanation:

a. The probability of a net profit of $80 is 3/38, and of a $20 loss is 35/38. Expected value  is calculated as the summation of both expectations:

$E(X)=P(x=win).E(x=win)-P(x=loss).E(x=loss)\\\\E(X)=80\times \frac{3}{38}-20\times\frac{35}{38}\\\\= -12.11$

Hence, the expected value is -12.11(a loss).

b. We calculate the expected value of 34 to determine which is better;

-From the question, E(X=34)= -$1.05,

-From a above, E(X=(00,0,1))= -$12.11

#-$1.05 is greater than -$12.11( by $11.06).

-Hence, it's better to bet on number 34 since it has the highest expected value of the two.