How Does Bayes theorem Work?

Bayes theorem helps us update our guesses based on new clues, like figuring out what toy you picked just by hearing it bounce.

Imagine you have a bag with two kinds of toys: bouncy balls and soft blocks. You pick one without looking, and it bounces. Now you want to know if it's more likely to be a bouncy ball or a soft block.

Let’s say:

• 60% of the toys are bouncy balls, and they always bounce.
• 40% are soft blocks, and only half of them bounce.

At first, you might think it's more likely to be a bouncy ball. But when it actually bounces, that gives you new info. Now you can say: "Okay, it bounced, so it must be one of the toys that bounce."

Out of all the bouncing toys:

• 60% of the total toys are bouncy balls, and they all bounce → 60% of the bouncing toys are bouncy balls.
• 40% of the total toys are soft blocks, but only half of them bounce → 20% of the bouncing toys are soft blocks.

So now you know it's more likely to be a bouncy ball, about 75% chance! That’s Bayes theorem at work: using clues to make smarter guesses. Bayes theorem helps us update our guesses based on new clues, like figuring out what toy you picked just by hearing it bounce.

Imagine you have a bag with two kinds of toys: bouncy balls and soft blocks. You pick one without looking, and it bounces. Now you want to know if it's more likely to be a bouncy ball or a soft block.