Probability runs from 0 to 1. Nought is impossible, one is certain, and a half is even chances.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Working one out
Count the outcomes you want, then divide by all the equally likely outcomes.
On a die
Rolling a 4 has 1 favourable outcome out of 6, so the probability is 1/6.
The rest of the story
Every outcome together sums to 1, so "not a 4" has probability 5/6.
Nought and one
A probability of 0 means the event cannot happen; 1 means it must. Everything real sits between, and most things sit well inside. Being able to place an event roughly on that scale before calculating is a useful instinct.
All outcomes sum to one
The probabilities of every possible outcome add to exactly 1, because something must happen. This is a strong check on any probability table: if the column does not sum to 1, something is missing or double-counted.
Words and numbers
"Likely", "unlikely" and "even chance" are vague; 0.7, 0.1 and 0.5 are not. Translating between the two is worth practising, because everyday language about risk is much less precise than people assume when they act on it.
The gambler's fallacy
A fair coin that has landed heads five times is still equally likely to land heads next. The coin has no memory. Believing that a run "must" end is one of the most persistent errors in probability, and it costs people real money.
Step 2: Try It Yourself
Tap and try it out.
favourable and the rest
1
5
all outcomes
?
The hatched bar is the piece the story is asking for.
Step 3: Watch an Example
One step at a time.
Watch Ana Work Out Two Probabilities
A bag holds 3 red and 5 blue counters.
- Step 1
She counts the total: 3 and 5 make 8.
Step 4: Your Turn
Practice makes it stick.
The Bag
Problem 1 of 2
2 red and 8 blue. Out of 10, how many outcomes are red?
The Certainty
Problem 2 of 2
What is the probability of an impossible event?
Out of How Many
1 of 4
A die. How many outcomes give an even number?
2 of 4
A die. How many outcomes in total?
3 of 4
What is the probability of a certain event?
4 of 4
4 green out of 10. How many are not green?
Step 5: Quick Check
Show what you know.
Question 1 of 1
A die. How many outcomes give a number above 4?
What You Learned
- A probability is a number from 0 to 1.
- It is the favourable outcomes divided by all the equally likely outcomes.
- All the outcomes together always add to 1.