Question

Snapdragon plants have a gene that determines the presence of chlorophyll. The dominant allele (C) causes the plant to make chlorophyll, while the recessive allele (c) makes none. Snapdragons that are homozygous dominiant (CC) are green, whereas those that are heterozygous (Cc or cC) are yellow. The homozygous recessive plants die almost immediately due to lack of chlorophyll. If a healthy adult snapdragon is chosen at random from a large population of offspring of a heterozygous cross, about 1/3 will have zero copies of the recessive, and 2/3 will have one copy. Let X be a RV that represents the number of copies of the recessive allele. Eight healthy Snapdragon plants were chosen at random from a large population of offspring of a heterozygous cross.

Answer 1

Answer: i)For X = (0,1) then P(x) = (1/3, 2/3)

ii) Then p=(2/3) as n=8

iii) 0.06828

Explanation:

Use binomial distribution:

Probability of being yellow (by having 1 recessive allele) is 2/3. This is a binomial distribution with p=2/3. And since there are 8 selections, our n is 8. So p=(2/3), n=8.

Recall that in binomial distribution P(X=x) = C(n,x) × p^x × (1-p)^n-x.

So for 3 out of 8, it means x=3 and n=8.

Our equation becomes P(exactly three Snapdragon are yellow) = P(X=3) = (8C3) × (2/3)³ × (1/3)5 = 0.06828