5 cards draw odds

Question

I have three cards of the same suit. What are the odds of receiving two more cards of the same suit? If the number of players is important, assume 5 players on the table.

Answer 1

This answer assumes you have no additional knowledge of the opponent's cards. You have five cards in your hand. Of those, three are spades and two are not spades, so you need two more spades to complete your flush. There are 47 cards that you haven't seen, and 10 of those 47 cards are spades. You discard the two non-spades. The odds of drawing two more cards that are spades are then:

(10 spades / 47 total cards) * (9 remaining spades / 46 total) = 0.213 * 0.196 = 0.042

You have about a 4.2% chance of completing your flush.