In: Statistics and Probability
Suppose you go to a local casino to gamble using a slot machine. The following probability distribution characterizes your net earnings on a single play. Assume each play is independent of the other and every play has this same distribution for earnings.
Net earnings ($) |
Probability |
-1.00 |
0.90 |
-0.50 |
0.07 |
5.00 |
0.0285 |
500.00 |
0.0015 |
You play this slot machine one hundred times. Assuming the central limit theorem, what is the chance that you will come out of the casino with a profit?
Let X = Net earning
Let's find the mean and standard deviation for one game by using the given probability distribution:
Where
Let's make table in excel:
From the above table we get
So the chance that you will come out of the casino with a profit is 0.4912 ( 49.12%)