select the correct games.\ntickets for all of the described charity raffle games cost $2 per ticket…

select the correct games.\ntickets for all of the described charity raffle games cost $2 per ticket. identify the games in which a person who buys a ticket for each game every day for the next 400 days could expect to lose less than a total of $200.\nthe 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.\nthe player picks a single letter from a to o 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 $240.\nthe player picks a single letter from a to e 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 $85.\nthe player picks a single letter from a to z 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 $338.\nthe 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.\nthe player picks a single letter from a to g 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 $84.

select the correct games.\ntickets for all of the described charity raffle games cost $2 per ticket. identify the games in which a person who buys a ticket for each game every day for the next 400 days could expect to lose less than a total of $200.\nthe 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.\nthe player picks a single letter from a to o 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 $240.\nthe player picks a single letter from a to e 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 $85.\nthe player picks a single letter from a to z 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 $338.\nthe 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.\nthe player picks a single letter from a to g 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 $84.

Answer

Explanation:

Step1: Calculate probability of winning for each game

For a game where the player picks a letter from a set of $n_{l}$ letters and a digit from 10 digits (0 - 9), the total number of possible combinations is $n = n_{l}\times10$. The probability of winning $P=\frac{1}{n_{l}\times10}$.

Step2: Calculate expected - value of winning per game

The expected - value of winning per game $E(X)$ is given by $E(X)=P\times\text{Winning amount}- \text{Cost of ticket}$. The cost of a ticket is $C = 2$ dollars.

Step3: Calculate expected total loss over 400 days

The expected total loss $L$ over 400 days is $L = 400\times(2 - E(X))$. We want $L<200$.

Game 1: Letter from A - J ($n_{l}=10$)

$P_1=\frac{1}{10\times10}=\frac{1}{100}$, $E(X_1)=\frac{1}{100}\times150 - 2=1.5 - 2=- 0.5$, $L_1 = 400\times(2-(-0.5))=400\times2.5 = 1000$

Game 2: Letter from A - O ($n_{l}=15$)

$P_2=\frac{1}{15\times10}=\frac{1}{150}$, $E(X_2)=\frac{1}{150}\times240 - 2=1.6 - 2=-0.4$, $L_2 = 400\times(2-(-0.4))=400\times2.4 = 960$

Game 3: Letter from A - E ($n_{l}=5$)

$P_3=\frac{1}{5\times10}=\frac{1}{50}$, $E(X_3)=\frac{1}{50}\times85 - 2=1.7 - 2=-0.3$, $L_3 = 400\times(2-(-0.3))=400\times2.3 = 920$

Game 4: Letter from A - Z ($n_{l}=26$)

$P_4=\frac{1}{26\times10}=\frac{1}{260}$, $E(X_4)=\frac{1}{260}\times338 - 2=1.3 - 2=-0.7$, $L_4 = 400\times(2-(-0.7))=400\times2.7 = 1080$

Game 5: Letter from A - T ($n_{l}=20$)

$P_5=\frac{1}{20\times10}=\frac{1}{200}$, $E(X_5)=\frac{1}{200}\times280 - 2=1.4 - 2=-0.6$, $L_5 = 400\times(2-(-0.6))=400\times2.6 = 1040$

Game 6: Letter from A - G ($n_{l}=7$)

$P_6=\frac{1}{7\times10}=\frac{1}{70}$, $E(X_6)=\frac{1}{70}\times84 - 2=1.2 - 2=-0.8$, $L_6 = 400\times(2-(-0.8))=400\times2.8 = 1120$

Since none of the calculated losses are less than $200$, there are no correct games.

Answer:

No correct games.