Suppose you have a DNA 10-mer. What is the probability that a randomly-generated
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Question
Suppose you have a DNA 10-mer. What is the probability that a randomly-generated 10-mer will match yours? Assume that each nucleotide can appear in a position in a DNA sequence with probability 1/4.
Note the following values for 4n:
How many times will a particular DNA 10-mer occur in a genome of 1 billion base pairs, assuming that each nucleotide occurs with the same probability (1/4)?
How many nucleotides long would a DNA sequence need to be in order for it to be found by chance no more than once in a genome whose size is 1 billion base pairs?
410 : 1 × 106 411 : 4 × 106 412 : 1.7 × 107 413 : 6.7 × 107 414 : 2.7 × 108 415 : 1 × 109 416 : 4.3 × 109 417 : 1.7 × 1010Explanation / Answer
What is the probability that a randomly-generated 10-mer will match yours:
The answer is 1/4 X 1/4 X 1/4 X 1/4 X 1/4 X 1/4 X 1/4 X 1/4 X 1/4 X 1/4 = 1/1048576
How many times will a particular DNA 10-mer occur in a genome of 1 billion base pairs, assuming that each nucleotide occurs with the same probability (1/4)?
(1/1048576) X 1000000000 => 0.00000095367431640625 X 1000000000 = 953.67431640625 = 954.
How many nucleotides long would a DNA sequence need to be in order for it to be found by chance no more than once in a genome whose size is 1 billion base pairs?
15 nucleotides long would a DNA sequence need to be in order for it to be found by chance no more than once in a genome whose size is 1 billion base pairs.
1/4 X 1/4 X 1/4 X 1/4 X 1/4 X 1/4 X 1/4 X 1/4 X 1/4 X 1/4 X 1/4 X 1/4 X 1/4 X 1/4 X 1/4 = 1073741824
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