Section 2 · Lecture 05 · Intro to Probability

Punnett Square

Two parent plants, each heterozygous (Aa) for flower colour, are crossed, and each passes on one allele at random. The random variable Y counts the dominant alleles the offspring receives.

The setup, in notation

Three different spaces, and the rule that connects them.

Outcome space, O {(A,A), (A,a), (a,A), (a,a)} — 4 equally likely allele combinations

Random variable, Y Y(allele 1, allele 2) = number of dominant (A) alleles in the offspring

Measurement space {0, 1, 2} — the possible values Y can take

Outcome space O

Each cell is one outcome: one allele from each parent, combined at random during fertilisation.

Rows = allele from Parent 1 · Columns = allele from Parent 2

Measurement space

{0, 1, 2} — the number of dominant alleles Y can take. Click one to see which outcomes in O map to it.

The distribution of Y

Bars fill in as you explore each value above.

Connecting to phenotype: since A is dominant, any offspring with Y ≥ 1 has purple flowers — only Y = 0 (genotype aa) is white. That gives the classic 3 : 1 phenotype ratio, built from this 1 : 2 : 1 genotype ratio.