October 2026 - Probability Study Guide

The basic calculation

Probability is favourable ÷ total. In a bag of 12 dressings where 3 are the wrong size, the probability of drawing a wrong one is 3/12, which is 1/4, 0.25, or 25%.

Two boundaries are worth holding onto: 0 means impossible, 1 means certain, and nothing outside that range is a probability. An answer choice above 1 or expressed as a percentage over 100 is wrong before you check the arithmetic.

And, or, and not

Independent or dependent

Whether the first event changes the second decides how the second probability is calculated.

• Independent — the first outcome does not affect the second. Coin tosses, dice rolls, or drawing an item and replacing it.
• Dependent — the first outcome changes what is available. Drawing an item and not replacing it: both the favourable count and the total fall.
• The phrase "without replacement" is the exam's signal that the second fraction must be recalculated.

With and without replacement

Theoretical against experimental

Theoretical probability is what the structure of the situation predicts: 1/6 for any face of a fair die. Experimental probability is what actually happened: 22 sixes in 100 rolls gives 0.22.

They differ, and they converge as the number of trials grows. A question asking why an experimental result does not match the theoretical one is usually answered by the size of the sample.

Terms to know

Outcome

A single possible result.

Event

An outcome or set of outcomes you are asking about.

Independent events

Events where the first does not affect the probability of the second.

Dependent events

Events where the first changes the probability of the second.

Complement

The probability that an event does not happen: 1 - P.

Mutually exclusive

Events that cannot both happen, so their probabilities can simply be added.

Theoretical probability

What the structure of a situation predicts.

Experimental probability

What was actually observed across a number of trials.

What the TEAS asks most

The same core ideas appear in different wording. If you can answer these without stopping to think, you have what this section requires.

Key points

• Probability is favourable outcomes over total outcomes, always between 0 and 1.
• And means multiply; or, with no overlap, means add.
• "Without replacement" changes both the numerator and the denominator of the second draw.
• The complement of an event is 1 minus its probability.
• Independent events have no memory of previous outcomes.