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. 2. ## Re: 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.

3. ## Re: Binomial Distribution

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?

4. ## Re: Binomial Distribution

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?

5. ## Re: Binomial Distribution

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

6. ## Re: Binomial Distribution

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.

7. ## Re: Binomial Distribution

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