Dice or cards or marbles in a bag are convenient ways to learn about
probability because both the total possible outcomes and the successful
outcomes are easily counted.
A die has six sides, so if you roll a die, each of the six numbers on it have
an equally likely possibility of being on top when the die stops rolling. So,
if you want to know the probability of getting a 6, there is one possible way
you would call 'success' and 6 total possibilities. The probability is
.
With two dice, you have 36 total possibilities, 6 of which are
where the dice total 7, so there is again
for a probability.
But there is only 1 way out of 36 to get snake eyes, so the probability of
rolling a 2 is
Cards work the same way, except that you just have more cards than sides of
a die. So the numbers are larger and the calculations more complex.
No matter what you are dealing with, probability is always a fraction, always
in the interval
, and always computed by figuring the number
of ways you can have a successful outcome and dividing that by the total
number of possible outcomes.