Question

For many years organize crime ran a number game that is now run illegally by many states government. the player select a three digit number from 000 to 999. there are 1000 such members. a bet of two dollars is placed on a number, say number 115. if the number is selected the player wins $700. if any other number is selected the player wins nothing. find the expected value for this game and describe what it means

Answer 1

Given

there are 1000 numbers from 000 to 999

Find

Expected value for this game

Explanation

as we have 1000 numbers from 000 to 999

probability to win = 1/1000

if the player wins the game , the amount he gains = $700 - $2 = $698

probability to lose the game = 1-1/1000 = 999/1000

if player loses the game , the amount he gains = -$2

therefore , the expected value =

$\begin{gathered} E(x)=\frac{1}{1000}\times698+\frac{999}{1000}\times(-2) \\ \\ E(x)=0.698-1.998=-1.3 \end{gathered}$

Final Answer

Hence , the expected value of the numbers game is -$ 1.3