Lessons · Medicine foundations · the Punnett square and Mendelian fractions
The Punnett square: four boxes, and the fractions fall out
Put one parent's two alleles along the top and the other parent's down the side, fill the four boxes, and every fraction the question wants is a count of boxes out of four.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
Genetics questions are almost always a fraction, and arguing with yourself about probabilities in your head is how a minute becomes five. Drawing four boxes takes ten seconds and the answer is then just counting, which is a thing you cannot get wrong under pressure.
How to think about it
Write the cross out. Fill every box by taking one letter from the top and one from the side. Then count only the boxes the question asked about, and say the answer as boxes out of four before you turn it into a fraction or a decimal.
Worked example
Aa × Aa: A and a across the top, A and a down the sideThe square is two by two because each parent gives one of two alleles.
The four boxes come out AA, Aa, Aa, aaEvery combination once. Aa appears twice, which is where the three to one comes from.
Boxes with at least one A: 3 of 4, so 3/4, or 0.75Counting, not reasoning.
Boxes that are aa: 1 of 4, so 1/4, or 0.25The other part of the same square.
Your turn
Aa crossed with aa gives the four boxes Aa, Aa, aa, aa. Write the aa share as a decimal.
2 of the 4 boxes are aa, so the share is
Solve one, graded on the server
The trap
Reading a 3 to 1 ratio as three out of three, or as a third. Three to one means three of four and one of four; ratios and fractions use the same numbers and mean different things, and the square settles it.