“and”
Both things must happen. In one table, find the shared cell. With two draws, multiply the chances along that path.
PROBABILITY WORKSHOP
Start with the group you are choosing from.
Probability tells us how likely something is. In these counting examples, write it as a fraction. First find what counts. Then find the whole group.
An event is the result we ask about. P(red) means the probability of red. A fraction has a top number (the numerator) and a bottom number (the denominator). A probability goes from 0, impossible, through 1, certain.
These tables use categories. Regression predicts a number from a pattern. R² is not a probability.
Begin with a source exampleTHE ONE QUESTION TO ASK FIRST
What is the whole group right now?
“or”
Either thing can happen. Add groups, then remove any overlap counted twice.
“given”
Stay inside the group named after “given.” That group is the denominator.
“not”
Find what is left. Subtract the event probability from 1, or count everything outside that group.
“without replacement”
The first choice changes what remains for the next choice.
WORKED NOTEBOOK EXAMPLES
Read the setup, then reveal one step.
CHECK THE ARITHMETIC
Choose the method that helps you learn.
A calculator can divide and multiply. It cannot decide which group is the denominator. Make that decision first.
Physical calculator directions are source checked and prepared. They are not device tested in this workshop.
PERSONAL PRACTICE
Build a new question, then reverse the formula.
Your quiz stays in this tab and starts over when you refresh the page. It is for your own learning and does not contact a tutor or cloud service. The optional calculator keeps its existing browser saved state.