to play the nickel game a player tosses two coins at the same time if both coins land tails then the player wins $1 if both coins land heads up then they win $2 suppose you play this game 12 times and it costs $1 to play how much money could a player win or lose explain your answer
expected return:
both tails = (1/4)($1) = $.25
both heads = (1/4)($2) = $.50
Since it costs $1.00 to play, the expected win is $75, so a loss of 25 cents per game
Then in 12 games .....
To determine how much money a player could win or lose in the nickel game, we need to calculate the possible outcomes and the corresponding win/loss amounts.
Since the game is played 12 times and each play costs $1, the total cost of playing all 12 times will be $1 * 12 = $12.
Let's analyze the possible outcomes of each play:
1. Both coins land tails (probability = 1/4): The player wins $1.
2. Both coins land heads (probability = 1/4): The player wins $2.
3. One coin lands heads and the other lands tails (probability = 1/2): The player loses $1.
Now, let's calculate the potential winnings or losses in each scenario:
1. Both coins land tails: The player wins $1 per play. Since this outcome has a probability of 1/4, the player can win $1 * (1/4) = $0.25 in each play. In 12 plays, the total potential winnings are $0.25 * 12 = $3.
2. Both coins land heads: The player wins $2 per play. With a probability of 1/4, the player can win $2 * (1/4) = $0.50 in each play. Over 12 plays, the total potential winnings are $0.50 * 12 = $6.
3. One coin lands heads and the other lands tails: The player loses $1 per play. Since this outcome has a probability of 1/2, the player can lose $1 * (1/2) = $0.50 in each play. In 12 plays, the total potential losses are $0.50 * 12 = $6.
To determine the overall amount of money a player can win or lose, we need to subtract the total cost of playing ($12) from the sum of the potential winnings ($3 + $6 = $9) and potential losses ($6).
Total potential winnings - Total potential losses - Total cost of playing
= $9 - $6 - $12
= $9 - $18
= -$9
Therefore, a player could potentially lose up to $9 in this game if they play 12 times.