Question

Tickets for all of the described charity raffles cost $2 per ticket. arrange the raffles in ascending order of their expected values to the player.

A. 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.
B. the 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.
C. 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.
D. the 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.
E. the 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.
F. the 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.

Answer 1

The expected values for each charity raffle are calculated and then arranged in ascending order. The ascending sequence of the raffles based on their expected values is C, E, A, B, F, D.

Step-by-step explanation:

Expected Value Calculation for Charity Raffles

We are asked to arrange the raffles in ascending order of their expected values to the player for the described charity raffles, where each ticket costs $2. To solve this mathematical problem completely, we calculate the expected value (EV) for each raffle option.

1. Calculate the total number of possible outcomes for each raffle.
   For example, Option A has 10 possible letters and 10 possible digits, so the total number of outcomes is 10 letters × 10 digits = 100 outcomes.
2. Compute the expected value using the formula EV = (probability of winning) × (prize amount) - (probability of losing) × (ticket cost).
3. List the calculated expected values and arrange them in ascending order.

Here's the calculation for each option:

• A. EV = (1/100) × $150 - (99/100) × $2 = $1.5 - $1.98 = -$0.48
• B. EV = (1/50) × $85 - (49/50) × $2 = $1.7 - $1.96 = -$0.26
• C. EV = (1/200) × $280 - (199/200) × $2 = $1.4 - $1.99 = -$0.59
• D. EV = (1/70) × $84 - (69/70) × $2 = $1.2 - $1.97 = -$0.77
• E. EV = (1/260) × $338 - (259/260) × $2 = $1.3 - $1.992 = -$0.692
• F. EV = (1/150) × $240 - (149/150) × $2 = $1.6 - $1.9867 = -$0.3867

Arranging the expected values in ascending order gives us: C, E, A, B, F, D.