Question

When playing roulette at a​ casino, a gambler is trying to decide whether to bet

​$1515

on the number

2727

or to bet

​$1515

that the outcome is any one of the

threethree

possibilities

00 comma 0 comma or 100, 0, or 1.

The gambler knows that the expected value of the

​$1515

bet for a single number is

negative 0.79 cents−0.79¢.

For the

​$1515

bet that the outcome is

00 comma 0 comma or 100, 0, or 1​,

there is a probability of

StartFraction 3 Over 38 EndFraction338

of making a net profit of

​$4545

and a

StartFraction 35 Over 38 EndFraction3538

probability of losing

​$1515.

a. Find the expected value for the

​$1515

bet that the outcome is

00 comma 0 comma or 100, 0, or 1.

b. Which bet is​ better: a

​$1515

bet on the number

2727

or a

​$1515

bet that the outcome is any one of the numbers

00 comma 0 comma or 100, 0, or 1​?

​Why?

Answer 1

The expected that using the outcome is probability expected value for the $15 0010 ori com be computed by distribution of pay off is X P(x=x) 45 3/38 -15 The expected pay off f(x) E(X) = 45* 15 * = 3:55263 - 3:8157894 = -10.26315 Therefore the expected valle of bet hele is -10-26315 b) clearly the $ is bet on the number 27 has an expected value 06 -079 which is greater Than –10.36315 Therefore clearly The $15 bet on the number 27 is better than the $15 on The outcome is any one of the number 00100Y 1.