Lessons · Teaching · probability, counted rather than felt
Probability is a count, not a feeling
The probability of an event with equally likely outcomes is the number of outcomes that count as success divided by the total number of outcomes. It is a number between 0 and 1, where 0 is impossible and 1 is certain, and it can be written as a fraction, a decimal or a percent.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
In beta. This lesson was written for Hone and has not yet been checked by a state certification officer. Practice material, not professional advice. What that means.
What it is for
'It is due' is the belief this lesson exists to kill. A coin that has landed heads five times has exactly the same one in two chance next throw, because the coin has no memory. Every lottery, every card game and every misread medical result runs on this misunderstanding.
How to think about it
Count the successful outcomes and count all the outcomes, and make sure every outcome you counted is equally likely. For two independent events happening together, multiply the two probabilities. Check that the answer sits between 0 and 1.
Worked example
One die: P(rolling a 4) = 1/6, one success out of six equally likely outcomesEqually likely is the condition that makes counting valid.
P(rolling an even number) = 3/6 = 1/2Three successes, six outcomes, then simplify.
Two coins both heads: 1/2 x 1/2 = 1/4Independent events multiply. The first throw tells you nothing about the second.
P(not an event) = 1 - P(event), so not rolling a 4 is 1 - 1/6 = 5/6Often much faster than counting the successes.
Your turn
Name the probability of an event that is certain.
A certain event has probability
Solve one, graded on the server
The trap
Believing a run changes the next outcome. After five heads, the sixth throw is still one in two. The coin does not know what it did before, and nothing is ever 'due'.