# Hidden Markov Model

I am trying to find answers to the following questions. Can someone please help. This is a Hidden Markov Model with 7 states and 4 observations. I have worked out the following solution but still need help with parts ii & iii.

Solution:

I. GATTAG = 1* 1 * 0.5 * 0.25 * 0.2 * 0.5 * 0.4 * 0.15 * 0.6 * 0.25 * 1 * 0.5 * 1 =0.00005625

II. GTAAG

possible paths: B -> S1-> S2 -> S4 -> S5 -> S7-> E

=>1 * 1 * 0.5 * 0.5 * 0.4 * 0.4 * 0.6 * 0.25 * 1 * 0.5 * 1 =

B -> S1-> S2 -> S4 -> S6 -> S7-> E

=> 1* 1 * 0.5 * 0.5 * 0.4 * 04 * 0.4 * 0 * 0.7 * 0.5 * 1 = 0

B -> S1-> S3-> S4 -> S6 -> S7-> E

=> 0

B -> S1-> S3-> S4 -> S5 -> S7-> E

=> 1 * 1 * 0.5 * 0.3 * 0.4 * 0.4 * 0.6 * 0.25 * 1 * 0.5 * 1 =

III. GTACGG

possible paths: B -> S1-> S2-> S3-> S4 -> S6 -> S7-> E

B -> S1-> S2-> S3-> S4 -> S5 -> S7-> E

B -> S1-> S3 -> S2-> S4 -> S6 -> S7-> E

B -> S1-> S3 -> S2-> S4 -> S5 -> S7-> E

B -> S1-> S3 -> S3-> S4 -> S6 -> S7-> E

B -> S1-> S3 -> S3-> S4 -> S5 -> S7-> E

B -> S1-> S3 -> S4 -> S6 -> S6 -> S7-> E

B -> S1-> S2 -> S4 -> S6 -> S6 -> S7-> E

How do I calculate this probability?