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

Question

When playing roulette at a? casino, a gambler is trying to decide whether to bet ?$55 on the number 32 or to bet $55 that the outcome is any one of the three possibilities

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

The gambler knows that the expected value of the ?$55 bet for a single number is

negative 0.26 cents?0.26¢. For the ?$55 bet that the outcome is 00, 0 , or 100, 0, or 1?, there is a probability of

StartFraction 3 Over 38 End Fraction338 of making a net profit of

?$15

and a

StartFraction 35 Over 38 EndFraction3538

probability of losing

?$55.

a. Find the expected value for the

?$55

bet that the outcome is

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

b. Which bet is? better: a

?$55

bet on the number

3232

or a

?$55

bet that the outcome is any one of the numbers

00 comma 0 comma or 100, 0, or 1??

?Why?

a. The expected value is

?$nothing.

?(Round to the nearest cent as? needed.)

b. Since the expected value of the bet on the number

3232

is

?

less

greater

than the expected value for the bet that the outcome is

00 comma 0 comma or 100, 0, or 1?,

the bet on

?

00, 0, or 1

the single number

is better.

Explanation / Answer

(A) E[x] = (3/38)*15 - (35/38)*5 = - 3.42?

B) Since the expected loss on single number is -0.26 cents which is lesser compred to -3.42 cents

thus a $55 bet on # 32 is better (lesser expected loss !)

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