for many years, organized crime ran a numbers game that is now run legally by many state governments. the…

for many years, organized crime ran a numbers game that is now run legally by many state governments. the player selects a three - digit number from 000 to 999. there are 1000 such numbers. a bet of $1 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 this means. the expected value of the numbers game is $ - 0.30. (round to the nearest cent.) choose the statement below that best describes what this value means, and if necessary, fill in the answer box to complete your choice. (round to the nearest cent.) o a. in the long run, the player can expect to lose $ for each game played. o b. in the long run, the player can expect to win $ for each game played. o c. in the long run, the player can expect to break even.

for many years, organized crime ran a numbers game that is now run legally by many state governments. the player selects a three - digit number from 000 to 999. there are 1000 such numbers. a bet of $1 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 this means. the expected value of the numbers game is $ - 0.30. (round to the nearest cent.) choose the statement below that best describes what this value means, and if necessary, fill in the answer box to complete your choice. (round to the nearest cent.) o a. in the long run, the player can expect to lose $ for each game played. o b. in the long run, the player can expect to win $ for each game played. o c. in the long run, the player can expect to break even.

Answer

Explanation:

Step1: Calculate probability of winning

The probability of winning $P(W)$ is $\frac{1}{1000}$ since there is 1 winning number out of 1000 possible numbers.

Step2: Calculate probability of losing

The probability of losing $P(L)$ is $1 - \frac{1}{1000}=\frac{999}{1000}$.

Step3: Calculate net - gain for winning and losing

The net - gain when winning is $700 - 1=699$ (subtracting the $1$ bet). The net - gain when losing is $- 1$.

Step4: Calculate expected value

The formula for expected value $E$ is $E = P(W)\times\text{Net - gain when winning}+P(L)\times\text{Net - gain when losing}$. So $E=\frac{1}{1000}\times699+\frac{999}{1000}\times(-1)=\frac{699 - 999}{1000}=\frac{- 300}{1000}=-0.30$. Since the expected value is negative, in the long run, the player can expect to lose money.

Answer:

A. In the long run, the player can expect to lose $0.30$ for each game played.