Fifteen Outs Example

   Pocket Cards                                                   Community Cards
Ace of Diamonds King of Diamonds                                         Two of Diamonds Six of Diamonds Nine of Hearts
"Flush Draw with Two Overcards"

You have the nut flush draw. You also think that it'd be nice to hit one of your two overcards. To make the flush or pair your pocket, you have fifteen outs. The nine remaining Diamonds, the three remaining Aces, and the three remaining Kings. Pretty good chances here. It would be a 31.915% chance to hit one of those on the turn. On the turn and river combined the chance is a good-looking 54.117%. Even if you don't hit it on the turn, you still have a 32.609% chance of hitting it on the river.

   Pocket Cards                                                   Community Cards
Eight of Spades Seven of Spades                                         Nine of Spades Two of Clubs Ten of Spades
"Outside Straight Flush Draw to a Straight or Better"

You don't have anything yet, but you do have fifteen cards left in the deck that'll improve you to at least a straight. Those fifteen outs would be the nine remaining Spades, the three non-spade Sixes, and the three non-spade Jacks. Why non-spade? Because we already counted them in our chances to make a flush. It's a common and easy mistake to make when you count certain outs twice, especially when a straight flush draw is involved. We're not doing it though! Your chance to hit any of those fifteen cards is the same as above.