# slot machine

• December 1st 2012, 05:48 AM
aloha
slot machine
Is it conditional probability or not? What is the result?

You walk into a Las Vegas casino. There are 10 slot machines. 9 of them win 20% of the time. 1 of them, the lucky machine, wins 30% of the time. But you don't know which one is the lucky one (the 30% winner). You watch someone put a quarter into the machine and win. What is the chance it was the "lucky" machine?
Express your answer as a fraction or as a decimal with 2 significant digits
• December 1st 2012, 06:09 AM
Plato
Re: slot machine
Quote:

Originally Posted by aloha
Is it conditional probability or not? What is the result?
You walk into a Las Vegas casino. There are 10 slot machines. 9 of them win 20% of the time. 1 of them, the lucky machine, wins 30% of the time. But you don't know which one is the lucky one (the 30% winner). You watch someone put a quarter into the machine and win. What is the chance it was the "lucky" machine?

The question asks for the probability of using the lucky machine given a win.

Or $\mathcal{P}(L|W)$. We know $\mathcal{P}(W)=\mathcal{P}(L\cap W)+\mathcal{P}(L^c\cap W)$.

As this is not a homework service, you must do the rest for yourself.
• December 1st 2012, 06:21 AM
aloha
Re: slot machine
I calculated P(L|W)= 1/10*30/100= 3/100.
I don't understand why you included the winning chance of the machines ? 1/10* 30% * 9/10*20% ?
• December 1st 2012, 06:28 AM
Plato
Re: slot machine
Quote:

Originally Posted by aloha
I calculated P(L|W)= 1/10*30/100= 3/100.
I don't understand why you included the winning chance of the machines ? 1/10* 30% * 9/10*20% ?

Well that is completely wrong. This is Bayesian conditioning question.

$\mathcal{P}(L|W)=\frac{\mathcal{P}(L\cap W)}{\mathcal{P}(L\cap W)+\mathcal{P}(L^c\cap W)}$.