November 2026 - Probability Study Guide for nursing students in
Probability is favourable outcomes over total outcomes, expressed as a fraction, decimal or percentage between 0 and 1. For independent events happening together, multiply the separate probabilities; for either of two outcomes, add them.
Try 4 short questions throughout this guide. Check each answer to learn from the explanation.
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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
Question
Operation
Example
Both A and B happen
Multiply
Two heads in two tosses: 1/2 × 1/2 = 1/4
Either A or B happens (no overlap)
Add
Rolling a 1 or a 2: 1/6 + 1/6 = 1/3
A does not happen
Subtract from 1
Not rolling a 6: 1 - 1/6 = 5/6
Question 1 of 4
A tray holds 4 red, 6 blue and 10 green tablets. What is the probability of selecting a blue tablet at random?
Choose one answer, then check it.
View the Answer and Explanation
Correct answer: A. 3/10
There are 20 tablets in total, so the probability is 6/20 = 3/10. 6/14 leaves the blue tablets out of the denominator, 1/6 inverts the relationship, and 1/3 would require 20 tablets with a different colour split.
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.
Question 2 of 4
A fair coin is tossed twice. What is the probability of two tails?
Choose one answer, then check it.
View the Answer and Explanation
Correct answer: B. 1/4
Both events must happen, so multiply: 1/2 × 1/2 = 1/4. Listing the four equally likely outcomes — HH, HT, TH, TT — confirms that only one of them is two tails.
With and without replacement
Worked example
A box holds 5 blue and 3 white swabs. What is the probability of drawing two blue swabs in a row, without replacement?
First draw: 5 blue out of 8 total, so 5/8.
Second draw: one blue is gone, so 4 blue out of 7 total — 4/7.
Multiply, because both must happen: 5/8 × 4/7 = 20/56.
Simplify: 5/14.
5/14, or about 36%. With replacement it would be 5/8 × 5/8 = 25/64, about 39% — the difference the phrase "without replacement" makes.
A run of past outcomes does not change the next independent one. After four heads, the probability of heads on the fifth toss is still 1/2. Questions test this directly, and the intuitive answer is the wrong one.
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.
What is the probability of drawing X?
Favourable over total, simplified, in the form the choices use.
What is the probability of both events happening?
Multiply — and check whether the first draw is replaced before writing the second fraction.
What is the probability that this does not happen?
One minus the probability that it does.
After several heads in a row, what is the chance of heads next?
Unchanged. Independent events have no memory.
Question 3 of 4
A die has been rolled four times, landing on 6 each time. What is the probability of rolling a 6 on the fifth roll?
Choose one answer, then check it.
View the Answer and Explanation
Correct answer: B. 1/6, unchanged
Rolls of a fair die are independent, so previous outcomes have no bearing on the next one — the probability stays 1/6. Both wrong intuitions come from imagining the die keeps a record, and while four sixes would be unusual, the question specifies a fair die.
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.
Question 4 of 4
A box holds 3 sterile and 7 non-sterile packs. Two are drawn without replacement. What is the probability that both are sterile?
Choose one answer, then check it.
View the Answer and Explanation
Correct answer: B. 1/15
The first draw is 3/10 and the second 2/9, since one sterile pack is gone from a smaller box, giving 6/90 = 1/15. 9/100 treats the draws as if the pack were replaced, and 3/10 is the probability of the first draw alone.
TEAS · Probability
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