Math Help Forum: Binomial Distribution

Consider a primitive slot machine which, for each quarter inserted, rewards the user with $10 with the probability 1/50. What is the probability of leaving with more money than one started if 100 quarters are inserted? Use the exact binomial distribution.

Originally Posted by fcabanski

Consider a primitive slot machine which, for each quarter inserted, rewards the user with $10 with the probability 1/50. What is the probability of leaving with more money than one started if 100 quarters are inserted? Use the exact binomial distribution.

So where exactly are you stuck? As a hint it will be easier if you use the compliment of the event.

I understand how to determine the number of "winning" pulls needed.

X = Y = 100
9.75X -.25Y >0

Need at least 3 X (winning) pulls to make more than is lost.

Then what?

Originally Posted by fcabanski

I understand how to determine the number of "winning" pulls needed.

X = Y = 100
9.75X -.25Y >0

Need at least 3 X (winning) pulls to make more than is lost.

Then what?

This leads to two questions. First, why is the hint in my first post useful. You said he needs at least 3 winning pulls so that you would need to calculate the probalibty that he wins 3 times, 4 times, .... 50 times. That would take a very long time. Second, what is the binomial distribution and what does it tell you? How would you use it to calculate the probability that the player wins exactly once?

I should take the BP of one or two losing spins, add those together, subtract from 1 (100%)

Originally Posted by fcabanski

I should take the BP of one or two losing spins, add those together, subtract from 1 (100%)

Yes but don't forget zero as well. You need zero wins 1 wins or 2 wins. Very nice.

I miswrote, but that's what I meant. Thanks for the help.