Probability is the language of uncertainty. The core aim of Science mastery is not to make students memorise fractions for coins and dice. It is to help them reason about what can happen, how likely each outcome is, and why repeated random events can still produce predictable long-run patterns.
For students and parents searching for probability in Science, probability rules, chance, random events, expected probability, genetics probability or how probability works, the most useful principle is this: probability does not predict exactly what will happen next; it describes how likely outcomes are under a defined model.
This distinction sits underneath statistics, genetics, risk, sampling and experimental inference.
The 60-Second Probability Scale
Probability ranges from:
0 — impossible
to
1 — certain
It can also be expressed as:
- fractions;
- decimals;
- percentages.
Example:
0.25 = 1/4 = 25%
Wait, What? A 70% Chance Does Not Mean the Event Must Happen 7 Times in the Next 10?
Correct.
Probability describes long-run tendency, not a fixed short-run schedule.
If an event has probability 0.7:
- it may happen 5 times out of 10;
- 8 times out of 10;
- even 10 times out of 10.
Across many repetitions, the observed proportion tends to become more stable.
Theoretical Probability
Theoretical probability comes from a model.
For equally likely outcomes:
Probability = favourable outcomes ÷ total possible outcomes.
Example:
A fair six-sided die.
Probability of rolling a 4:
1/6.
Experimental Probability
Experimental probability comes from observed data.
Example:
A seed germinates in 82 of 100 trials.
Estimated experimental probability:
82/100 = 0.82.
With more trials, the estimate may become more stable.
Independent Events
Two events are independent when the occurrence of one does not change the probability of the other.
For independent events:
P(A and B) = P(A) × P(B).
Example:
Two independent fair coin tosses.
Probability of two heads:
1/2 × 1/2 = 1/4.
Mutually Exclusive Events
Mutually exclusive events cannot occur together.
Example:
On one die roll:
- rolling a 2;
- rolling a 5.
For mutually exclusive events:
P(A or B) = P(A) + P(B).
Conditional Probability
Conditional probability asks:
What is the probability of A given that B has already occurred?
This is written:
P(A | B).
Conditional probability is central to:
- medical testing;
- genetics;
- Bayesian reasoning;
- risk assessment.
Probability in Genetics
Simple inheritance problems often use probability to predict offspring genotypes or phenotypes.
For example, if each parent contributes one allele independently under a simple Mendelian model, Punnett squares represent possible combinations and their probabilities.
Real genetics can be much more complex, but probability provides the foundation.
A Worked Example: Genetic Cross
Suppose a simple model gives:
Probability of recessive phenotype = 1/4.
This does not mean every family of four children must contain exactly one child with that phenotype.
Each birth is a separate event under the model.
Long-run frequencies approach the expected probability across many births.
Probability and Risk
Risk combines probability with consequence.
Two events can have the same probability but very different seriousness.
Example:
- 10% chance of a minor inconvenience;
- 10% chance of severe harm.
The probabilities match.
The risks do not.
Probability and Sampling
Random sampling relies on probability.
Each unit has a defined chance of selection.
This helps reduce systematic selection bias.
See Scientific Sampling.
Probability and Statistical Significance
Statistical significance uses probability models to assess how unusual observed data would be under a null hypothesis.
This is not the same as asking the probability that the null hypothesis is true.
Probability and Normal Distribution
A normal distribution assigns probability across a continuous range of values.
The area under the curve corresponds to probability.
See Normal Distribution.
Expected Value
Expected value is the long-run average outcome under a probability model.
For a fair die:
(1 + 2 + 3 + 4 + 5 + 6) ÷ 6 = 3.5.
You can never roll 3.5 on one die.
Expected value is a long-run average, not a guaranteed single outcome.
Primary Science Probability Foundations
Primary learners can practise:
- impossible, unlikely, likely and certain;
- fractions and percentages;
- simple repeated trials;
- genetic probability at an age-appropriate level.
Secondary Science Probability
Secondary students should increasingly connect probability to:
- genetics;
- sampling;
- risk;
- normal distributions;
- hypothesis testing;
- conditional probability.
How to Practise
For any probability problem:
- define the event;
- define the sample space;
- decide whether events are independent;
- calculate the probability;
- interpret what the number means in context.
Common Probability Mistakes
- assuming short runs must match expected percentages exactly;
- confusing independent with mutually exclusive events;
- adding probabilities when multiplication is required;
- treating expected value as a guaranteed outcome;
- confusing p-values with the probability a hypothesis is true.
Frequently Asked Questions
What is probability?
Probability is a numerical measure of how likely an event is under a defined model.
What is the range of probability?
From 0 for impossible to 1 for certain.
What is experimental probability?
It is the observed frequency of an event divided by the number of trials.
What is conditional probability?
It is the probability of one event given that another event has occurred.
Why is probability important in Science?
It underlies uncertainty, genetics, sampling, risk and statistical inference.
Useful eduKateSG Routes
The Core Aim
Probability gives Science a disciplined language for uncertainty.
Define the event. Model the possibilities. Calculate the likelihood. Interpret it as a tendency, not a promise.
That is the core aim: reason clearly about chance without confusing uncertainty with randomness without structure.
Properly taught kids shine a bright light into the future.