.
The base composition of a certain microbial genome is pG =
pC = 0.3 and pA = pT = 0.2. We are interested in 2-words where the letters
are assumed to be independent. There are 4 × 4 = 16 2-words.
(a) Present these 16 probabilities in a table. (Do your 16 numbers sum to
1.0?)
(b) Purine bases are defined by R = {A, G} and pyrimidine bases by Y = {C, T}.
Let E be the event that the first letter is a pyrimidine, and F the event
that the second letter is A or C or T. Find P(E), P(F), P(E ∪F), P(E ∩F),
and P(Fc).
(c) Set G={CA, CC}. Calculate P(G | E), P(F | G ∪ E), P(F ∪ G | E).