Given that the marble I draw is red, what is the probability it was drawn from the 1st bag?

I have 2 bags, each containing 3 marbles.
The 1st bag contains 2 red marbles and white marble.
The 2nd bag contains 40 red marbles (and no white marbles).
I pick a bag at random and draw a marble at random from it.
Given that the marble I draw is red, what is the probability it was drawn from the 1st bag?

Hay,

I'm going to be up front with you. I can help you draw this stuff, but it's never going to come close to the masterpiece of what you would have done given no instruction, placed in a true vacuum from the age of 7, and only fed dehydrated rice cakes with hydraulic fluid coating. I just want you to be aware of the greatness you could have achieved and the heights you could have reached later to plummet from.

OK, let's start by drawing a clear marble. There, good job. Yes, you are right you didn't draw anything. If you are having a tough time with this concept I want you to look at the air. Do you see it's clarity? now look at a clear piece of tape (put it over your eyelid) you can;t see the clear parts of it, get it?

OK now, lets draw a red one. Start with half of a circle (this should be a square, if you don;t understand that concept, you need help with some other math, that I can't get into right now... get it?) OK, so start with the half circle (wink, wink) if you need a reference, get a lemon and cut it in half. Place half of it on the table and shove the other half on your red marker as an eraser (It will erase the invisible ink you used to draw the clear marble, so be careful...)

Now that you have drawn half of the circle, fold the paper in half and cut it into 50ths (I know people say you can only fold a piece of paper 15 times, but considering you haven't really drawn anything yet, you should be able to fold it at least 30 times which gets you halfway there, if you were folding it instead of cutting it.)

Finish the red marble and tape it in a spherical shape (a sphere is just a circle in a time-warp). Tape it with the tape on your eyelid. In your eye if you can.

Now we need to deal with the dimension jump inside your second bag. I see you are having the problem where 3 marbles are 40 inside of a closed system. It's no big deal but the probability you'll get out of it unscathed is 1:1099923. the 40 red marbles will especially cause problems. It's really a shame you didn't think to fill the second bag with 3 clear marbles, because in that dimension they become a harmless used car salesman.

Anyway jump into the bag, and you should land right back in your seat. Now jump into the first bag and draw a new red marble in there. You just bumped the probability up to 1:1, good job Schroedinger, get it?

Source(s):
I am Schroedinger's cat.

I am eating a sandwich that both has mayonnaise and also does not.