select the correct answer.\na state offers two lottery games, winone and playball. both games cost $2 per…

select the correct answer.\na state offers two lottery games, winone and playball. both games cost $2 per ticket.\n- in winone, the player picks a single letter from a to j and a single digit from 0 to 9. if both the letter and the digit match the letter and the digit picked on that day, the player wins $150.\n- in playball, the player picks a single letter from a to t and a single digit from 0 to 9. if both the letter and the digit match the letter and the digit picked on that day, the player wins $280.\nif the cost of a playball lottery ticket were changed to $1 and the prize to $250, what would the expected value be?\na. -$0.85\nb. -$0.25\nc. $0.25\nd. $0.75

select the correct answer.\na state offers two lottery games, winone and playball. both games cost $2 per ticket.\n- in winone, the player picks a single letter from a to j and a single digit from 0 to 9. if both the letter and the digit match the letter and the digit picked on that day, the player wins $150.\n- in playball, the player picks a single letter from a to t and a single digit from 0 to 9. if both the letter and the digit match the letter and the digit picked on that day, the player wins $280.\nif the cost of a playball lottery ticket were changed to $1 and the prize to $250, what would the expected value be?\na. -$0.85\nb. -$0.25\nc. $0.25\nd. $0.75

Answer

Explanation:

Step1: Calculate the probability of winning

There are 20 letters (from A - T) and 10 digits (from 0 - 9). The total number of possible combinations is $20\times10 = 200$. So the probability of winning, $P(W)=\frac{1}{200}$.

Step2: Calculate the probability of losing

The probability of losing, $P(L)=1 - P(W)=1-\frac{1}{200}=\frac{199}{200}$.

Step3: Calculate the net - gain for winning and losing

The cost of a ticket is $C = 1$ and the prize is $P = 250$. The net - gain for winning, $G_W=250 - 1=249$. The net - gain for losing, $G_L=- 1$.

Step4: Calculate the expected value

The formula for expected value $E$ is $E=P(W)\times G_W+P(L)\times G_L$. Substitute the values: $E=\frac{1}{200}\times249+\frac{199}{200}\times(-1)$. First term: $\frac{1}{200}\times249=\frac{249}{200}$. Second term: $\frac{199}{200}\times(-1)=-\frac{199}{200}$. Then $E=\frac{249 - 199}{200}=\frac{50}{200}=0.25$.

Answer:

C. $0.25$