What is probability? Probability is a measurement of how likely it is that something will happen. All probabilities are numbers between 0 and 1 (inclusive). An event which could not possibly happen has a probability of 0 (zero). An event which is guaranteed to happen has a probability of 1 (one).

Any event which could happen, but which is not guaranteed to happen, has a probability somewhere between zero and one, but not including either of those numbers.

If an event's probability is close to zero, it is unlikely to happen. If an event's probability is close to one, it is likely to happen.

If an event is equally likely to happen or not happen, its probability is 0.5, or .

Here are some examples of different probabilities. Note that in some of these the word "random" or "randomly" is used. "Randomly" basically means, without any planning, knowledge or strategy. For example, if I'm playing rock-paper-scissors with you, and you choose to always pick rock, or if you choose to alternate in sequence, you are using a strategy. If you can read my mind to know which I'll pick, you are using knowledge.

Zero Probability Example
Suppose you have eight dollars. I have a five dollar bill, a ten dollar bill, and a one dollar bill. I blindfold you and ask you to randomly* pick a bill. What is the probability that you will now have ten dollars?

Answer: The only way you could have ten dollars is if you took a two dollar bill from me. Since I didn't have a two dollar bill, that's not possible. Since the event is not possible, the probability is 0.

Low Probability Example
Suppose I am holding a jar which contains 1000 green jelly beans, and 1 yellow jelly bean. I blindfold you, and then ask you to pick a jelly bean randomly. Is the probability of you getting the yellow jelly bean going to be closer to zero, or to one?

Answer: It will be closer to zero. With so many green jelly beans in the jar, it seems very likely that you would pick one of those instead of the yellow one.

0.5 Probability Example
I flip a coin. What is the probability that it will come up heads?

Answer: We generally say that a coin is "fair," which means it's equally likely to land on either side. Since the event is equally likely to happen or not happen, it has a 0.5 probability of happening.

High Probability Example
Suppose I am holding a hat which contains all the letters from A to Z, and I ask you to pick one of them (blindfolded again).  Is the probability that you'll get a consonant closer to one or closer to zero?

Answer: There are far more consonants than vowels, so you're likely to get a comsonant. Thus, the probability is closer to one.

In the scenarios below, state whether the probability is 0, 1, 0.5, unlikely (closer to zero than one), or likely (closer to one than zero). Assume that each scenario is random.

1.

The number six is showing on a six-sided die

2.

An odd number is showing on a six-sided die

3.

The number seven is showing on a six-sided die

4.

I flip a coin four times, and it shows heads each time

5.

I pick a crayon from a 64-color crayola crayon box, and the color I pick is not white

6.

I pick a letter from the alphabet, and it is either a consonant or a vowel

7.

I shuffle a deck of cards, and when I draw the first card, it is the ace of spades

8.

I shuffle a deck of cards, and when I draw the first card, it is not a diamond

9.

I shuffle a deck of cards, and when I draw the first card, it is red

10.

I pick a positive integer, and it is composite