Bayes' theorem and tree diagrams

[qwertyuiopasd]

There are two slot machines. The probability of winning with machine 1 is 0.1 and the probability of winning with machine 2 is 0.5. If you try a machine at random, lose and want to play again, should you switch?
I tried using Bayes' theorem and the result is that there is a higher chance of having picked machine 1, so you should switch. But when I made a tree diagram, I get the same probability of winning the second time whether you switch or not. Can anyone explain?

 

[Steven G]

If you want us to find your mistake then it would be best if you show us your work. If you followed the guideline of this forum by posting your work you would have received help by now.

I tried using Bayes' theorem and the result is that there is a higher chance of having picked machine 1, so you should switch.You lost me here. You know that machine 1 give a higher chance of winning. The thing is you do not know which machine is number 1. But according to you Bayes' theorem says that you probably are using machine 1, so why would you switch.

Personally as soon as I thought that I was playing machine 1 I would stick with it as I would have twice the chance of winning compared to machine 2. Do you understand that??

 

[qwertyuiopasd]

Bayes' theorem says I have probably picked machine 1, which has a 10% chance of winning. Because machine 2 has a 50% chance of winning, which is 5 times as likely as machine 1, it is preferable to switch.

 

[pka]

There are two slot machines. The probability of winning with machine 1 is 0.1 and the probability of winning with machine 2 is 0.5. If you try a machine at random, lose and want to play again, should you switch?
I tried using Bayes' theorem and the result is that there is a higher chance of having picked machine 1, so you should switch.

This question is far too vague. Surely you do not know which slot is which? For if you did why pick slot #1? Moreover, we assume that its equally likely that you chose either slot first. You chose to mention Bayes' theorem, so the I infer that having lost you would like to know the probability that you indeed chose slot I.
$\mathcal{P}(I|L)=\dfrac{\mathcal{P}(L|I)}{\mathcal{P}(L|I)+\mathcal{P}(L|II)}$$=\dfrac{(0.9)(0.5)}{(0.9)(0.5)+(0.5)(0.5)}=\dfrac{9}{14}$

 

[Steven G]

Bayes' theorem says I have probably picked machine 1, which has a 10% chance of winning. Because machine 2 has a 50% chance of winning, which is 5 times as likely as machine 1, it is preferable to switch.

Sorry I thought that it said 0.05 for machine 2.