10 different kinds of amino acids, which we will call A,B, C, D, E, F, G, H, I, and J. Charles creates a protein consisting of a sequence offour amino acids by first randomly selecting a type of amino acid for the first position,then randomly selecting a type of amino acid for the second position, then randomlyselecting a type of amino acid for the third position, and finally randomly selecting atype of amino acid for the fourth position. For each position in the sequence, each ofthe ten types of amino acids is equally likely to be selected. A type of amino acid canappear at more than one position in the sequence, so a sequence like (B, J, A, B) ispossible.Luis has four amino acids, and wants to make a copy of Charles’ sequence. Luiscan do this if any permutation of his amino acids matches Charles’ sequence.What is the probability that Luis can match Charles’ sequence, if Luis’ amino acidsare:(a) G, H, I, J(b) G, H, I, I(c) H, H, I, I(d) H, I, I, IExplain why you use each formula. Show your calculations. Express all answers to thenearest ten-thousandth.

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Author:Amos Gilat
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10 different kinds of amino acids, which we will call A,
B, C, D, E, F, G, H, I, and J. Charles creates a protein consisting of a sequence of
four amino acids by first randomly selecting a type of amino acid for the first position,
then randomly selecting a type of amino acid for the second position, then randomly
selecting a type of amino acid for the third position, and finally randomly selecting a
type of amino acid for the fourth position. For each position in the sequence, each of
the ten types of amino acids is equally likely to be selected. A type of amino acid can
appear at more than one position in the sequence, so a sequence like (B, J, A, B) is
possible.
Luis has four amino acids, and wants to make a copy of Charles’ sequence. Luis
can do this if any permutation of his amino acids matches Charles’ sequence.
What is the probability that Luis can match Charles’ sequence, if Luis’ amino acids
are:
(a) G, H, I, J
(b) G, H, I, I
(c) H, H, I, I
(d) H, I, I, I
Explain why you use each formula. Show your calculations. Express all answers to the
nearest ten-thousandth.

 
 
 
 
 
 
 
 
 
 
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