EasterMath: festive riddle search!

The MathCityMap team wishes you a Happy Easter and is curious to see if some of you have hidden the Easter eggs this year with the help of an exciting trail. MathCityMap is certainly one of the best apps to combine Easter with math and fun.

As a thank you for our great community, we have come up with an Easter special: an Easter riddle with a little surprise. The solutions can be sent to gogesch@math.uni-frankfurt.de with the subject “EasterMath” by April 14, 2024 and the first three correct answers will receive a small surprise from the MathCityMap team by post.

We hope that we can make everyone happy with the puzzle and some with the surprise.

The riddle:

The Easter Bunny wants to train his Easter Bunny apprentices and comes up with a delightful riddle. He takes two identical Easter baskets and paints 10 chocolate Easter eggs with green paint and 10 foam Easter eggs with red paint.
He gathers everyone together and says: “You can divide all the eggs between the two baskets however you like. Tomorrow you have to pull an egg out of one of the two baskets blindfolded. If you draw a chocolate Easter egg, you will advance to the next training level.”

How do the Easter bunny apprentices have to distribute the Easter eggs so that the chance of advancement is particularly high? How high is the probability then?

(based on: Eder, H.-K. (2020). Zauberhafte Mathematik – Mathematische Rätsel und Knobeleien. Munich: Hanser.)