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An inbred strain of plants has a mean height of 24cm. A second strain of the same species also has a mean height of 24cm. When these plants are crossed the F1 are also 24cm in height.However, when the F1 are crossed the F2 plants show a wide range of heights, the greatest number are similar to P1 and F1 but apprx. 4 out of 1000 are only 12cm tall and 4 of 1000 are 40cm tall. What fraction of the F2 plants will be apprx. 28cm in height ?

a)3/4

b)9/16

c)56/256

d)none

The answer given is c).

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  • $\begingroup$ I know that a and b can not be the answer. $\endgroup$ – biogirl Sep 10 '13 at 18:07
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    $\begingroup$ A simple google search will reveal this website where that exact question was asked half a year ago. $\endgroup$ – Amory Sep 10 '13 at 19:39
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    $\begingroup$ Totally unrelated comment: If it is 24 cm high, I doubt it is a tree. $\endgroup$ – skymningen Sep 12 '13 at 11:18
  • $\begingroup$ @skymninge done the edit ! $\endgroup$ – biogirl Sep 12 '13 at 12:36
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From the source that Amory cites :

You know that the number of offspring is shown by Pascal's triangle, right?

For two alleles you have 1 : 2 : 1

For three alleles 1 : 3 : 3 : 1

For four 1 : 4 : 6 : 4 : 1 etc.

So, if 4 in 1000 are 12 and 36 cm tall, that means that every in 250 plants is tall like that. And on which level of Pascal's triangle you have sum of 250? For two alleles: 1 + 2 + 1 = 4 For threee: 1 + 3 + 3 + 1 = 8 For four: 1 + 4 + 6 + 4 + 1 = 16 etc. until 1 : 8 : 28 : 56 : 70 : 56 : 28 : 8 : 1 Here you see that you have 9 options of height. The difference is 36 cm - 12 cm = 24 cm. 24 cm /9 = 3 cm, so 1 plant will 12 cm, 8 plants will be 15 cm, 28 plants will be 18 cm, 56 plants will be 21 cm, 70 plants will be 24 cm (i.e. "the majority of F2 are like P1 and F1") and 56 plants will be 27 cm tall out of 250 plants. Thus C is the closest.

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