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 $ 4bet, 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?

a) - $0.169

b) - $0.04242

Step-by-step explanation:

Data provided in the question:

Bet amount = $4

Probability of losing $4 =

Probability of gaining $4 =

a) The expected value

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

= $4 × - $4 ×

= $4 ×

= - $0.169 (Negative sign means loss)

b) The amount lost for each dollar =

=

= - $0.04242

0 is its x and y coordinate