At a carnival you play a ring toss game 30 times. It's a dollar to play and your chances of winning are 15%. What are your expected winnings
What do you win?
What a sucker you would be to play this game!
the expected winnings on one play is 15 cents.
You are playing this 30 times, so your can expect to win $4.50 , but you spent $30 to play those games.
To calculate the expected winnings, we need to multiply the probability of winning by the amount won for each game, and then sum up those values.
Given:
- Number of times playing the game (n) = 30
- Cost to play the game (c) = $1
- Probability of winning each game (p) = 15% = 0.15
Let's assume the winnings for each game are as follows:
- If you win, you get a prize worth $5, so the winnings for a win (w) = $5
- If you lose, you get no prize, so the winnings for a loss (l) = $0
Now, let's calculate the expected winnings.
Expected winnings = (probability of winning x winnings for a win) + (probability of losing x winnings for a loss)
Expected winnings = (p x w) + ((1 - p) x l)
Expected winnings = (0.15 x $5) + (0.85 x $0)
Expected winnings = $0.75 + $0
Expected winnings = $0.75
Therefore, your expected winnings for playing the ring toss game 30 times would be $0.75.