Pea plants contain two genes for seed color, each of which may be Y (for yellow seeds) or G (for green seeds). Plants that contain one of each type of gene are called heterozygous. According to the Mendelian theory of genetics, if two heterozygous plants are crossed, each of their offspring will have probability 0.75 of having yellow seeds and probability 0.25 of having green seeds.
a. Out of 10 offspring of heterozygous plants, what is the probability that exactly 3 have green seeds?
b. Out of 10 offspring of heterozygous plants, what is the probability that more than 2 have green seeds?
c. Out of 100 offspring of heterozygous plants, what is the probability that more than 30 have green seeds?
d. Out of 100 offspring of heterozygous plants, what is the probability that between 30 and 35 inclusive have green seeds?
e. Out of 100 offspring of heterozygous plants, what is the probability that fewer than 80 have yellow seeds?