someone please explain these 2 questions. the answers are listed, i just need th

Question

someone please explain these 2 questions. the answers are listed, i just need the explanations on why. TY.

1) If R = any purine, Y = any pyrimidine, and N = any nucleotide, what is the probability of finding the sequence 5 GRANTY 3 in any molecule of DNA? Assume nucleotides are in equal percentages.
1/64

1/128

Correct Answer
1/256

1/1024

1/4096

2) Which of the following DNA molecules is the most thermodynamically stable?

5’GGGGAAAACCCCTTTT 3’
3'CCCCTTTTGGGGAAAA 5’

5’AGCGCGCAGCGTTTTT 3’
3’TCGCGCGTCGCAAAAA 5’

5’AAAGGAATTCCGTTAA 3’
3’TTTCCTTAAGGCAATT 5’

5’AAAAAAGGGGGGTTTT 3’
3’TTTTTTCCCCCCAAAA 5’

Correct Answer

5’GCATCGAGGCCGGCTG 3’

3’CGTAGCTCCGGCCGAC 5’

Explanation / Answer

1. The correct answer is 1/256. See the desired sequence is GRANTY.

Here the chances for first nucleotide that is G = 1/4 (since total no. of nucleotide is 4 that is A, T, C, and G).

The chances for R is 1/2 (since 2 out of 4 are purine and 2 pyrimidine. Hence the chances for any purine is 50% that is 1/2).

The chances for third nucleotide (A) is 1/4 (since total no. of nucleotide is 4).

N is any nucleotide hence the probablity for N is 100% that is 1.

The chances for T = 1/4 (since total no. of nucleotide is 4) and

The chances for Y = 1/2 (because 2 out of four nucleotides are pyrimidine hence the chances for any pyrimidine = 50% that is 1/2.

Now by multiplication of all the probability we can find the probability for whole sequence that is

1/4 x 1/2 x 1/4 x 1 x 1/4 x 1/2 = 1/256

2. The most thermodynamically stable is last one because of the more number of C-G base pairing (11). C-G base pairing occurs through tripple bond while A-T base pairing occurs via double bond. Hence the sequence in which more number of tripple bond occurs will be more stable.

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