Exact chances of embryos

Embryos are transferred, and each has the same chance of implanting, on its own. You will list every outcome with exact fractions, and find some chances. The model is made up for learning.

The idea. For $m$ embryos, there are $2^m$ outcomes. Each embryo either implants (1) or does not (0). The chance of an outcome is the product of the chances of its parts.

Your tasks.

1. Finish outcomes. It gives a dictionary: for each number of embryos that implant, the chance of that number.
2. Finish at_least. It gives the chance that k or more embryos implant.
3. Finish expected. It gives the expected number that implant.