Question

Two players, A and B, roll a dice with random outputs between 1 and 30. The player with the higher number wins, and the loser pays the winner the amount that the winner gets on his dice. What is the expected winnings? Would you prefer being player A or player B? Why?

Answer 1

To find the expected winnings, calculate the expected value for each player by summing up the products of each possible outcome and its corresponding probability. The player with the higher expected winnings would be preferred.

Step-by-step explanation:

To find the expected winnings, we need to calculate the expected value for each player. Let's consider player A first. The probability of rolling any number from 1 to 30 is equal, so each number has a 1/30 chance of being rolled. Player A's expected winnings can be calculated by summing up the products of each possible outcome and its corresponding probability:

Expected Winnings for Player A = (1/30) * 1 + (1/30) * 2 + ... + (1/30) * 30

Similarly, we can calculate the expected winnings for player B:

Expected Winnings for Player B = (1/30) * 1 + (1/30) * 2 + ... + (1/30) * 30

After calculating the expected winnings for both players, we can compare them to determine which player would be preferred. The player with the higher expected winnings would be the preferred player.