Question

A boardwalk game of chance costs $1 to play. you have a 25% chance of winning $1 back, a 20% chance of winning $2 (your $1 back, plus an additional $1), and a 10% chance to win $5 (a gain of $4). what is the expected value of playing the game if you lose your bet 45% of the time?

Answer 1

Expected value of playing the game  = $0.8

What is cost ?

• Cost denotes the amount of money that a company spends on the creation or production of goods or services.
• It does not include the markup for profit. From a seller's point of view, cost is the amount of money that is spent to produce a good or product.

   

Cost of playing = $2

Expected return

10% chance to win $1 = $1  10% = $0.1

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

50% chance to win $5 = $5  50% = $2.5

15% chance to lose $2 (being cost) = $2  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 game = $2.8 - $2 = $0.8

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