① Simple probabilityNo calculator
Probability = number of ways it can happen ÷ total number of equally likely outcomes.
Practice questions
② Complementary eventsNo calculator
The probabilities of an event happening and not happening add up to 1 (or 100%).
Practice questions
③ Expected outcomesCalculator useful
Expected number = probability × number of trials.
Practice questions
④ Relative frequencyCalculator useful
Relative frequency = number of times it happened ÷ total number of trials.
Practice questions
⑤ Two events togetherNo calculator
List all the equally likely outcomes, then count the ones you want.
Practice questions
Challenge questions
Unknown totals, changing a bag, and two picks with or without replacement
Key steps
Probability is always between 0 (impossible) and 1 (certain). Write it as a fraction in its simplest form.
Not happening: \(P(\text{not }A)=1-P(A)\).
Expected number = probability × number of trials.
Two events: list every equally likely outcome so you do not miss any. Without replacement, the total goes down by one.