A player picks random cards from an ordinary card deck, without returning them to the deck. How many cards should he pick so as to get at least one ace with 70% probability?
I was reading the computer program assisted respective "table of probability" and "simulated result" methodology by Charlie and Penny, and decided to perform a verification with the calculations done by the aid of an online solver.
VERIFICATION
Case 1: 14 cards
When we pick 14 cards, the probability of NOT having a single ace is:
comb(48,14)/comb(52,14)
= 2109/7735
So, the probability of having at least a single ace
= 5626/7735
~ 0.727343245
Case 2: 13 cards
When we pick 13 cards the probability of NOT having a single ace is:
comb(48,13)/comb(52,13)
= 6327/20825
So, the probability of having at least a single ace
= 14498/20825
~ 0.696182473
Since in the latter case, 100*(required probability) rounds to 70, while in the former case it rounds to 73, we must conclude that the player must pick precisely 13 cards.
Edited on April 7, 2022, 11:35 pm
Puzzle Solution Verification
