Page 103 - Probability Demystified

92 CHAPTER 5 Odds and Expectation

Probability Sidelight

PROBABILITY AND GENETICS

An Austrian botanist, Gregor Mendel (1822–1884), studied genetics and used
probability theory to verify his results. Mendel lived in a monastery all of his
adult life and based his research on the observation of plants. He published
his results in an obscure journal and the results remained unknown until the
beginning of the 20th century. At that time, his research was used by a
mathematician, G. H. Hardy, to study human genetics.
Genetics is somewhat more complicated than what is presented here. How-
ever, what is important here is to explain how probability is used in genetics.
One of Mendel’s studies was on the color of the seeds of pea plants. There
were two colors, yellow and green. Mendel theorized that each egg cell and
each pollen cell contained two color genes that split on fertilization. The
offspring then contained one gene cell from each donor. There were three
possibilities: pure yellow seeds, pure green seeds, and hybrid-yellow seeds.
The pure yellow seeds contain two yellow genes. The pure green seeds
contained two green genes. The hybrid-yellow seeds contain one yellow gene
and one green gene. This seed was yellow since the yellow gene is dominant
over the green gene. The green gene is said to be recessive.
Next consider the possibilities. If there are two pure yellow plants, then the
results of fertilization will be YY as shown.
Y Y
YYY YY
YYYYY
Hence, PðYYÞ¼ 1:

The results of two pure green plants will be gg.
g g
g gg gg
ggggg

Hence, P(gg) ¼ 1.
What happens with a pure yellow and a pure green plant?
g g
YYg Yg
Y Yg Yg
Hence, P(Yg) ¼ 1.