Roll a die 100 times. the casino pays 2to 1. you have a 12 in 38 chance to win. the sum could be ___ give or take___
The sum of what?
the sum of the draws... basically the net gain
It depends upon how much is bet each time.
If you bet 1 dollar each time, there is a 26/38 = 0.6842 chance you will lose it,and a 12/38 = 0.3158 chance you will win $2, for a dollar gain of 0.6316.
There is a net loss expectation of 0.6842 - 0.6316 = 0.0526 per toss. That would be $5.26 after 100 tosses.
To find the sum of the payout, we first need to calculate the probability of winning and the expected value.
The probability of winning can be calculated using the equation:
Probability of winning = (Number of favorable outcomes) / (Total number of possible outcomes)
In this case, the probability of winning is given as 12 out of 38. So, the probability of winning is 12/38.
Next, we calculate the expected value of the payout using the equation:
Expected value = (Probability of winning) * (Payout if win) + (Probability of losing) * (Payout if lose)
The payout if win is 2 times the original wager (2:1), and the payout if lose is 0.
Let's plug in the values:
Expected value = (12/38) * (2) + (26/38) * (0)
Simplifying, we find:
Expected value = 24/38
To calculate the sum, we multiply the expected value by the number of times we roll the die (100).
Sum = (Expected value) * (Number of rolls) = (24/38) * (100)
Simplifying further, we get:
Sum = 2400/38 = 63.16 (approximately)
Therefore, the sum of the payout, on average, would be approximately 63.16.
Note: Since we are using an average, the actual sum you could win may vary.