molecular biology - Proportion of amino acids from a random polymer of U and C

A protein synthesis assay was carried out in vitro. A polyribonucleotide containing U and C in proportion 1:5 (positions of U and C are random) was used as a template. Which amino acids and in what proportions will be incorporated into the synthesized polypeptide molecules?

А. 1Phe : 5Pro : 3Leu.

B. 1Leu : 1Pro : 1Ser : 1Phe.

C. 1Phe : 5Ser : 5Pro : 5Leu.

D. 1Phe : 25Pro : 5Ser : 5Leu.

E. 5Leu : 5Pro.

First thing I am not sure is whether only U and C is there. I have tried solving this sum taking both the conditions into consideration . I also tried solving it from options but could not succeed.

Answer

The first thing to mention is that this is the type of experiment that Marshall Nirenberg performed in order to break the genetic code, and for which he got the Nobel prize in 1968. We stand on the shoulders of giants.

If the ratio is U:C, 1:5, then it is easy to calculate the probability of encountering each of the 8 possible codons composed by just U and C. So for example:

the probability of UUU is (1/6)³

the probability of UUC is (1/6)²*(5/6)

and so on.

Here's a Table that gives all of the values and demonstrates that the answer is (D).