Find the probability that the number of intermediate offspring is less than or equal to the mode.
Suppose that the alleles A and a for height are additive, meaning that plants with genotype AA are tall, plants with genotype Aa are intermediate, and those with genotype aa are short. If an Aa plant is crossed with another Aa plant, 1/4 of the offspring should be tall, 1/2 should be intermediate, and 1/4 should be short. Assuming that the other conditions for the binomial distribution are met, find the probabilities of the following if a cross produces six offspring.