Question

Now, the bin contains 12 green balls. In each event, you pick one ball from the bin and observe the color of the ball. The balls are only distinguishable with their colors. After observation, you put the ball back into the bin. What is the entropy value for five events in bits?

Answer 1

Answer:

Note that the probability of no two balls having the same color is equivalent to all three balls having different colors. The probability of this event is

521⋅720⋅919=376

Because on the first step we want to pick a red ball, which has probability of 521, on the second step we want to pick a green ball, and on the third step we want to pick a blue ball. The order in which we pick the balls doesn't matter, which is reflected in the (associative) multiplication: 5/21⋅7/20=7/21⋅5/20, etc.

Is this right? I'm sceptical of my answer. I wrote a script to test my answer, and it appears that the probability should be just a little under 14, which sounds much more reasonable.