How do I determine the probability I will draw three or more cards with a value of 9 or higher from a standard deck of cards when drawing 5 cards?

Question

Replacement should not be used.

Jokers are removed, Aces=1, Jacks=11, Queens=12, and Kings=13

Answer 1

The fastest way to solve would be the following: 9, 10, J, Q, and K are 9 are higher; 4 suits means selecting 3 out of 5 or more from 9 or higher when there are 20 of 52 that are 9 of higher; we can use combinatorics, but faster is to use the cumulative from the hypergeometric distribution.

To avoid needing to subtract probabilities, selecting 3 or more from 20 of 52 means selecting 2 or less from 32 of 52

In Excel, we use = hypgeom.dist(2,5,32,52,1) - the final 1 means cumulative, 2 or less

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