Examples

• When you toss a coin in the air, what are the chances it will land with the head up? It's a matter of probability. You can probably guess that the chances of the coin landing with the heads up is 50-50, or 1 out of 2.
• When you roll a die, what are the chances it will stop with a 3? A die has six sides, so the probably if rolling any given number (1 through 6) is 1 in 6.
• Suppose you have a deck of 52 playing cards. What are the chances of pulling any card and having it be the ace of spades? The chances are 1 in 52.

Those are examples of theoretical probability. When you actually try it — toss a coin a thousand times, roll a die a couple hundred times, or pull a card at random a couple dozen times — you will find that the actual figures differ slightly from the theoretical figures. For example, you might find the coin coming up heads 520 times out of a thousand. Theoretically, it should be 500 out of 1000. In the same way, if you roll a die 500 times, you might find it actually comes up with a 5.

Single Events

YOu have three marbles that are totally identical except for their color. One is red, one is blue, and the third is green. If you close your eyes, shuffle them around, and pick one:

What are your chances of picking a red marble? 1 in 3.

What are your chances of picking a red or blue marble? 2 in 3.

What are your chances of picking a red, blue, or green marble? 3 in 3, or 100%

What are your chances of picking a yellow marble? 0 out of 3. No chance, because there is no yellow marble.

Compound Events