Albino animals are well known, but what about plants? Apiron and Zohary (1961) found a recessive mutation in orchard grass (Dactylis glomerata) that causes a chlorophyll deficiency. Individuals with two deficient copies of the gene lack the green pigment entirely (and die), but heterozygous individuals, which have one normal copy of the gene and one deficient copy, appear to produce normal levels of chlorophyll. Using progeny testing, the authors found that 12 of 47 plants sampled from the Matzleva Valley in Israel were heterozygotes. Assume that the plants were randomly sampled.

a. What probability distribution should we use to calculate the probability of obtaining a specific number of heterozygous individuals (p) in a random sample of size 47?

b. Write the formula for the likelihood of p, given the data. What does the likelihood measure?

c. Write the formula for the log-likelihood of p.

d. Calculate the log-likelihood of the value p=0.50, given the data.