The probability is the total number of ways that X can happen divided by Y. The mathematical formula looks like this:
number of ways to get event X/number of all possible events (Y)
The probability of getting a heart dealt to you randomly from a deck of cards is 1/4. There are 13 hearts in a deck of cards, and there are 52 cards total in a deck. 13/52 is the actual probability, but like any fraction, it can be reduced to its simplest form.
There are different ways to describe a probability than using a fraction. You could also use a decimal. 1/4 is the same thing as 0.25. You could use a percentage. 1/4 is the same thing as 25%. Or you could say that it will happen 1 in 4 times, or you could state it as odds. 3 to 1 against.
And here's one more probability rule that's REALLY important. The probability of a multiple events equals the probabilities of the individual events multiplied by each other. So if you flip two coins, the probability of them BOTH landing on heads is 1/2 times 1/2, or 1/4. Stated in odds terms, thats 3 to 1 against. If you roll two dice, the probability of getting "snake eyes", or two 1's, is 1/6 times 1/6, or 1/36. Stated in odds terms, that's 35 to 1 against.
One more thing to remember. If something happens before something else, it doesn't affect the probability of the next event. In other words, if you're playing roulette, and the ball has landed on 00 five times in a row, the odds of it landing on 00 the sixth time is still an independent event, and is still 1 chance in 38, or 37 to 1 against. No more, no less. If you flip a coin ten times in a row, and get heads every time, on the 11th flip, the odds of getting heads are still even odds, or 1/2. No more, no less.
See also: Probability, Odds, Expectations, and the House Edge
