Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 1 or a 6, nothing otherwise. What is your expected value?
-1.33?
yes. or, to be more exact, -4/3
-3 + 1/3 * 5 = ?
Thank you!
Well, let's do the math. If you roll a 1 or a 6, you'll get $5.00, but if you roll any other number, you'll get nothing. So, the probability of rolling a 1 or a 6 is 2 out of 6 (or 1/3).
So, the expected value can be calculated as follows:
Expected value = (Probability of winning × Winning amount) - (Probability of losing × Losing amount)
Expected value = (1/3 × $5.00) - (2/3 × $3.00)
Expected value = $1.67 - $2.00
Oh, dear! It looks like you've stumbled upon a clown's nightmare. With an expected value of -$0.33, it seems that, on average, you'll end up losing a little bit of money. Just remember, it's all in the spirit of clownish fun!
To find the expected value, we need to determine the probability of each outcome and multiply it by the corresponding payoff.
For this scenario, rolling a 1 or 6 has a payoff of $5.00, while rolling any other number has a payoff of $0.00. Since it is a fair die, there is an equal chance of rolling any number from 1 to 6, so the probability of rolling a 1 or 6 is 2/6 (or 1/3), and the probability of rolling any other number is 4/6 (or 2/3).
Now, let's calculate the expected value:
Expected Value = (Probability of 1 or 6) * (Payoff of 1 or 6) + (Probability of any other number) * (Payoff of any other number)
Expected Value = (1/3) * $5.00 + (2/3) * $0.00
Expected Value = $5.00/3 + $0.00
Expected Value = $5.00/3
So, the expected value in this case is $5.00/3, which is approximately $1.67.