A numbers game run by many state governments allows a player to select a three-digit number from 000 to 999. There are 1000 such numbers. A bet of $5 is placed on a number. If the number is selected, the player wins $500. If any other number is selected, the player wins nothing. Find the expected value for the game.

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joaobezerra joaobezerra · Answer 1 · 2021-01-23T01:36:59+01:00

Answer:

The expected value for the game is of -$4.5

Step-by-step explanation:

The expected value of the game is given by each scenario multiplied by its probability.

Scenario 1: Player wins

1 correct number from a set of 1000, so probability of 1/1000.

In this case, the player spent $5, but earns $500, so a net of 500 - 5 = $495

Scenario 2: Player loses

Probability of 999/1000.

In this case, the player loses $5.

So, the expected value for the game is:

[tex]E = \frac{495*1}{1000} - \frac{5*999}{1000} = -4.5[/tex]

The expected value for the game is of -$4.5