Question

When you give $4 for a bet in a casino​ game, there is a 258/495 probability that you will lose $4 and there is a 237/495 probability that you will make a net gain of $4. ​(If you​ win, the casino gives you $ 4and you get to keep your $ 4​bet, so the net gain is $4.)
(a)- What is your expected​ value?
(b)-In the long​ run, how much do you lose for each dollar​ bet?

Answer 1

Answer:

a) - $0.169

b) - $0.04242

Step-by-step explanation:

Data provided in the question:

Bet amount = $4

Probability of losing $4 = $\frac{258}{495}$

Probability of gaining $4 = $\frac{237}{495}$

a) The expected value

= Winning amount × winning probability - Losing amount × Losing probability

= $4 × $\frac{237}{495}$ - $4 × $\frac{258}{495}$

= $4 × $\frac{237-258}{495}$

= - $0.169 (Negative sign means loss)

b) The amount lost for each dollar = $\frac{\textup{Expected Value}}{\textup{Bet amount}}$

= $\frac{\textup{-0.169}}{\ \textup{4}}$

= - $0.04242