Player A and B invented a new game. The probability for Player A to win a round is 1/3 and the probability that Player B will win a round is 2/3. To make the game fair, Player A will score 3 points when he/she winds a round and Player B will score 2 points when he/she wins. How many times per round can each player expect to score? That is, what is the expected value for each player?

Question

Player A and B invented a new game. The probability for Player A to win a round is 1/3 and the probability that Player B will win a round is 2/3. To make the game fair, Player A will score 3 points when he/she winds a round and Player B will score 2 points when he/she wins. How many times per round can each player expect to score? That is, what is the expected value for each player?

please help me

^^i really need help with this question^^

To help you understand the question let's assume each player plays 12 games.
Player A, according to your probability should win 4 games, and at 3 points a game should get 12 points
Player B should win 8 games. and at 2 points per win should have 16 points.

The "expected value" = Probability * payback
for player A expected value = 1/3 * 3 = 1
for player B expected value = 2/3 * 2 = 4/3

Answer 1

To determine the expected value for each player, we can multiply the probability of each player winning a round by the number of points they score when they win.

For Player A:
Probability of winning a round = 1/3
Points scored per win = 3
Expected value for Player A = (1/3) * 3 = 1

For Player B:
Probability of winning a round = 2/3
Points scored per win = 2
Expected value for Player B = (2/3) * 2 = 4/3

Therefore, Player A can expect to score 1 point per round on average, while Player B can expect to score 4/3 (or approximately 1.33) points per round on average.