Probability of independent events

• Each birth is an independent event.
• If two carrier parents have a 25% chance of an affected child, then after a first affected child the chance of the second child being affected is still 25%.
• To find the chance of two particular outcomes in two separate children, multiply: chance of two affected children in a row = 1/4 × 1/4 = 1/16.

Worked example 9: a Punnett square from a ratio

• A pea plant with round seeds is crossed with a plant with wrinkled seeds.
• In the offspring, 48 plants have round seeds and 52 have wrinkled seeds (close to 1 : 1).
• What are the genotypes of the parents?
• A 1 1 ratio appears in a cross between a heterozygote and a homozygous recessive: Rr × rr.
• The wrinkled offspring (rr) prove that the round parent had an r allele, so it was Rr.

Worked example 10: expected numbers

• If two hybrid tall pea plants (Tt × Tt) produce 400 seeds that all grow, about how many plants are expected to be short?
• Short = tt = 1/4 of 400 = 100 plants; tall = 300 (of which about 100 are TT and 200 are Tt).
• Real counts usually differ a little from the expected numbers because fertilisation is a matter of chance, but with large numbers the results come close to the predicted ratio.
• That is why Mendel’s use of hundreds and thousands of plants gave clear results.

Linking the ideas

• Genes (DNA) are the cause; the inherited traits are the effect.
• Variation within a population (different alleles) is the raw material on which natural selection works. Without variation there is nothing to select.
• Artificial selection uses the same variation, but the human breeder decides which individuals reproduce.
• Genetic diseases show what can happen when a harmful recessive allele becomes homozygous; communities reduce this through awareness, screening and counselling, which also respects human differences and protects the health of future generations.