Question

A boardwalk game of chance costs $2 to play. You have a 10% chance of winning $1 back, a 25% chance of winning back your entire $2 chance to play, and a 50% chance to win $5. What is the expected value of playing the game if you lose your bet 15% of the time?

Answer 1

Answer:

Thus, expected value of playing = $2.8 - $2 = $0.8

Explanation:

Cost of playing = $2

Expected return

10% chance to win $1 = $1 $\times$ 10% = $0.1

25% chance to win back $2 = $2 $\times$ 25% = $0.5

50% chance to win $5 = $5 $\times$ 50% = $2.5

15% chance to lose $2 (being cost) = $2 $\times$ 15% = ($0.3)

= $0.1 + $0.5 + $2.5 - $0.3 = $2.8

Now for this we have to pay fixed cost $2

Thus, expected value of playing = $2.8 - $2 = $0.8