In pea plants, plant height, seed shape, and seed color are governed by three in
ID: 189731 • Letter: I
Question
In pea plants, plant height, seed shape, and seed color are governed by three independently assorting genes. The three genes have dominant and recessive alleles, with tall (T) dominant to short (t), round (R) dominant to wrinkled (r), and yellow (G) dominant to green (g).
Part D
What proportion of the F2 are expected to be TtRRgg? (Hint: Consider the probability of obtaining each genotype for the three genes separately and then use the product law.)
Express your answer using three decimal places.
Explanation / Answer
Answer : 1/64
If you crossed two heterozygous individuals (Pp x Pp), you will get a 3:1 ratio Or, you get a 1:2:1 ratio genetically of PP, Pp and pp respectively. 1+2+1 = 4, the number of genetically possible offspring.
Now, if you crossed two heterozygous individuals for two unlinked traits (PpQq x PpQq), you'd get a 9:3:3:1 ratio phenotypically. 9+3+3+1 = 16m the number of genetically possible offspring. Interstingly, enough, this is sort of like the binomial expansion of (3x+1)^2, which is 9x^2 + 2(3)(1)x + 1, or 9x^2 + 3x + 3x + 1.
Now, crossing two heterozygous individuals for three unlinked traits (TtRrGg x TtRrGg, in your case) would yield a 54:3:3:3:1 phenotypic ratio, or a 27:9:9:9:3:3:3:1 genotypic ratio. the sum of either sets of numbers equals 64, the total possible number of genetic offspring. now, this looks like the cubic binomial expansion of 3X+1: (3x+1)^3 = 27x^3 (all phenotypically dominant organisms, with or without heteozygote trait(s) ) + 9x^2 (all organisms dominnant for 2 traits and recessive phenotypically for 1) + 3x (recessive two and dominant for one) + 1 (recessive for all three). These powers of 3 follow with what I've shown up before.
TTRRgg is only 1 out of the 64 organisms, look at TtRrGg x TtRrGg, the F2 cross. take each individual and cross:
Tt x Tt -> 1/4 chance of Tt
Rr x Rr -> 1/4 chance of RR
Gg x Gg -> 1/4 chance of gg
total probability is 1/4 * 1/4 * 1/4 = 1/64.
1/64 = 0.016 to 3 decimal places