1/52
and then if you guess again without replacing the card, the denominator lowers.
So:
3 of hearts! 1/52
(2 of clubs tossed out)
... oh dang, um, well jack of spades, 1/51..
etc.
as long as you don't guess a card that's been tossed out (in which case its 0% lol)
4 out of 52
3/4
There are four 9's and 48 non-9's. The odds against a 9 is 48 to 4.
If you put the one card back in before trying it the second time, then the odds are slightly worse; otherwise, the odds are the same - it does not matter if you pull two cards at once or one card twice, subject to the noted limitation.
Since half of the cards (26 of the 52) are a red card (hearts and diamonds) the odds are 1 in 2 (or 50%) that any given card will be red.
The odds against drawing a 10 out of a 52 card deck are 12:1.
4 out of 52
It's easy enough to GUESS a card without looking at it. Pick any card. Ok, I guess its the 3 of Diamonds. Done. However, guessing a card, or sequence of cards correctly, is a bit trickier. Lets assume that we are going to use a standard deck of cards (52, no Jokers) and you will pick one at a time, and I will guess what it is. In this example, we're going to assume that you return the card to the deck. This is an important clarification as it drastically changes the probabilities. The first time, I have a 1/4 chance of guessing the suit, a 1/13 chance of guessing the value, and a 1/52 chance of guessing both correctly. The second time, the chances of me getting the card correct are again 1 in 52, however, getting both guesses right means I have a 1 in 2704 chance (52 x 52). The third time, again, I have a 1 in 52 chance of guessing the card correctly, but to get the whole sequence correct, my odds have reduced to 1 in 140608 (52 x 52 x 52). And so on. Being able to guess even the first 6 cards correctly is a rather astounding feat, but is not in and of itself significant. Just like someone winning the lotto, there's always a chance of "beating the odds". But it does grow exponentially less likely. When you do see someone who manages this feat MULTIPLE times, you are probably dealing with some sort of trick: a marked deck, a forced series of cards or some other factor that you aren't aware of.
7 to 1
7:1
From a 'standard' deck of 52 cards - the odds that you will draw a card of any single suit is 1 in 4.
If you assume that the Ace is high, then the odds of drawing a card higher than a nine is a standard deck of 52 cards is 20 in 52, or 5 in 13, or about 0.3846. If you assume that the Ace is low, then the odds of drawing a card higher than a nine is a standard deck of 52 cards is 16 in 52, or 4 in 13, or about 0.3077.
12 in 13
Assuming a full, regular deck, no jokers? There are 52 cards in such a deck, 26 red and 26 black, making the odds of drawing a red card exactly 1 in 2.
The probability of drawing a queen or a four from a standard 52 card deck is 8 in 52, or 2 in 13, or about 0.1538.
For a dingle card drawn at random, it is 1/4.
3/4