# Bayes Theorem vs. simple math

#### charles2000

##### New member
Hi everybody,

I just encountered Bayes theorem and I can't seem to understand the logic behind it. This because of the conflict with common sense.

For instance: if I have a sack with four marbles in it, three black and 1 red, the chances on picking a red one out are... 0,25.
Now I have a friend that gives me advice on which marble to pick: I pick one out, hold it in my fist, and he advises me whether to throw it back or not (not seeing the color himself). This advice is pretty worthless, but nonetheless: in 25% of the cases he will be right when advising me to choose the red one.

Here's the "paradox" however... If I did the math correctly then the chances on picking a red marble out of the sack after the advice of my friend is (0.25 x 0.25)/(0.25/0.25 + 0.75x0.75)=0.1. But this is obviously not true... It should be 0.25...

I'm guessing it must have to do with actions being independent from each other or something like that, but I cannot think of a reason why I should use basic statistics for the marble problem + advice and Bayes Theorem when it comes to weather forecasts/desease spreading etc. I guess I miss the meaning of a basic concept here...

All help is welcome!

Kind regards,
Charles

#### daon2

##### Full Member
Hi everybody,

I just encountered Bayes theorem and I can't seem to understand the logic behind it. This because of the conflict with common sense.

For instance: if I have a sack with four marbles in it, three black and 1 red, the chances on picking a red one out are... 0,25.
Now I have a friend that gives me advice on which marble to pick: I pick one out, hold it in my fist, and he advises me whether to throw it back or not (not seeing the color himself). This advice is pretty worthless, but nonetheless: in 25% of the cases he will be right when advising me to choose the red one.

Here's the "paradox" however... If I did the math correctly then the chances on picking a red marble out of the sack after the advice of my friend is (0.25 x 0.25)/(0.25/0.25 + 0.75x0.75)=0.1. But this is obviously not true... It should be 0.25...

I'm guessing it must have to do with actions being independent from each other or something like that, but I cannot think of a reason why I should use basic statistics for the marble problem + advice and Bayes Theorem when it comes to weather forecasts/desease spreading etc. I guess I miss the meaning of a basic concept here...

All help is welcome!

Kind regards,
Charles
if you choose to follow your friend's advise, you are nothing more than the claw, and he the player. I do not understand your application of the theorem, or maybe i don't understand the game.