An interactive companion to the BIOL 200 probability lecture. It lets students explore relative frequency, the OR / AND / NOT rules, ABO blood-type inheritance and empirical tables by clicking, simulating and checking the math step by step.
Open the interactive: Probability Basics
- Open the link in any modern browser (desktop, tablet or phone). Nothing to install or log in to.
- The five tabs across the top follow the order of the lecture. Press the keys 1 to 5 to jump between tabs, which is handy when presenting.
- The Dark background / Light background button switches the color scheme. The dark version matches the lecture slides.
- Every tab ends with a short Try it list of steps for students to work through.
- Each calculation is shown in full, so students can follow how the answer is reached, not just see the final number.
Estimates a probability as a relative frequency, p = x/n, where x is the number of times the event happens and n is the number of trials. Students choose an experiment (a coin landing heads, a die rolling a 6, or a die rolling an odd number) and add 1, 10, 100 or 1,000 trials. A running chart shows the estimate after every trial against the true probability. The chart shows that small samples jump around and large samples settle close to the true value.
Shows that OR means add and NOT means subtract from 1. There are two modes.
- One die: students click the faces that count as a success. The tool adds the 1/6 probabilities and shows the NOT version (1 − P).
- Deck of cards: students pick two events (for example Queen and Heart). The deck and a Venn diagram highlight the cards in A only, B only and both. The tool then works through P(A or B) = P(A) + P(B) − P(A and B), showing why cards in both events would otherwise be counted twice. Picking events with no overlap shows that mutually exclusive events can simply be added.
Shows that AND means multiply for independent events, using all 12 outcomes of rolling a die and flipping a coin. Students click dice and coin faces to choose the events, and the matching outcomes turn gold. The gold block's width times its height is the multiplication rule. A simulate button rolls and flips up to 1,000 times so students can compare the counted frequency with the calculated answer. A summary card sums up the OR, AND and NOT rules.
Applies the rules to ABO blood-type inheritance. Students choose each parent's genotype, and a Punnett square shows every allele combination.
- Each box is an AND: this allele from one parent and that allele from the other, ½ × ½ = ¼.
- Each blood type is an OR of its boxes, so its boxes are added together.
Clicking a blood type highlights its boxes. The tool also calculates the chance that two children share a blood type, and can simulate 100 children to compare with the expected proportions.
Explains what an empirical table is: real counts from a sample, where probabilities come from counting a cell and dividing by the total. For any cell, it compares two answers side by side:
- the multiplication rule, using only the row and column totals
- the empirical count, using the number actually in the cell
A dot grid draws every individual in the sample so students can see the cell, its row and its column. The tab has three data sets.
- Blood type O and handedness: unrelated traits, so both methods agree (independent).
- Fruit flies, body color and wing shape: linked genes on the same chromosome, so the methods disagree and the table is the one to trust.
- Your own numbers: editable counts and labels for building examples in class.
An optional setting shows the count the multiplication rule predicts in every cell.
- The data in the empirical tables are illustrative, built to demonstrate the concepts, and are not from a published study.