A probability runs from 0 to 1. Zero means impossible, one means certain, and everything real sits between.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Theoretical probability
When outcomes are equally likely, probability is favourable outcomes divided by total outcomes.
Experimental probability
This is what actually happened: successes divided by trials. It rarely matches the theory exactly.
They converge
The Law of Large Numbers says that over many trials the experimental value closes in on the theoretical one.
A famous trap
Five heads in a row does not make tails "due". A coin has no memory, and each toss stays at one half.
The complement
The probability an event does not happen is 1 minus the probability it does. For "at least one", this is usually the fastest route.
From zero to one
Probability measures likelihood on a scale from 0 for impossible to 1 for certain. Any value outside that range signals an error, which makes it a useful check on every calculation.
The equally-likely assumption
Counting favourable outcomes over total outcomes works only when all outcomes are equally likely. A loaded die breaks the assumption, and so does almost any real-world situation worth studying.
The complement
The probability of not happening is 1 minus the probability of happening. When "at least one" appears in a question, computing the complement — none at all — is almost always the shorter route.
Probability is a long-run frequency
A probability of 0.5 says that over very many repetitions about half will succeed. It says nothing about the next trial, which is why a run of heads does not make tails more likely.
Step 2: Try It Yourself
Tap and try it out.
Red
Blue
Green
Blue has the most. It has 3 more than Green.
Step 3: Watch an Example
One step at a time.
Watch Priya Use the Complement
Priya rolls two dice and wants the probability of at least one six.
- Step 1
Counting the ways to get at least one six is fiddly, so she counts the opposite instead.
Step 4: Your Turn
Practice makes it stick.
The Bag
Problem 1 of 2
A bag has 3 red and 7 blue marbles. What is the probability of red, as a decimal?
The Complement
Problem 2 of 2
The probability of rain is 0.35. What is the probability of no rain?
How Likely?
1 of 8
One die. Probability of a six, as a decimal to three places?
2 of 8
One die. Probability of an even number, as a decimal?
3 of 8
P(A) = 0.2. What is P(not A)?
4 of 8
A bag has 4 red and 6 blue. Probability of blue, as a decimal?
5 of 8
20 trials gave 13 successes. Experimental probability, as a decimal?
6 of 8
Five heads in a row. Probability the next toss is tails, as a decimal?
7 of 8
Sort each probability by what it describes.
Tap something to move it.
- Empty
- Empty
8 of 8
What is the probability of an impossible event?
Step 5: Quick Check
Show what you know.
Question 1 of 2
P(A) = 0.45. What is P(not A)?
Question 2 of 2
After four heads, what is the chance of heads next?
What You Learned
- Probability runs from 0 to 1.
- Theoretical probability counts outcomes; experimental probability counts results.
- The complement rule turns "at least one" into a single subtraction.