Wow! I didn’t just tangle this. I royally scrambled it. (I inverted the binomials, too)
I’m glad you are here to unscramble the sacred ball’s of Excalibur.
In your “other method” you multiplied the binomials but added the results. I assume for this method that you add binomials, because you are counting, and for the first method, you multiply the probabilities. Is that a correct assumption?
This is a broad question, but when do you use the harmonic mean to find “overall” probability?
Thank you, Miss Melody.