Question

An ion channel can be in either open (O) or closed (C) states. If it is open, then it has probability 0.1 of closing in 1 microsecond; if closed, it has probability 0.3 of opening in 1 microsecond. Calculate the probability of the ion channel going through the following sequence of states: COO. An individual can be either susceptible (S) or infected (I), the probability of infection for a susceptible person is 0.05 per day, and the probability an infected person becoming susceptible is 0.12 per day. Calculate the probability of a person going through the following string of states: SISI.

Answer 1

a) P (COO) = 0,135

b) P ( SISI) = 0,00015

Explanation:

a) the probability of an ion channel in open position is 50 % 0,5

the probability of an ion channel in close position is 50 % 0,5

probability for the following sequence of states COO

to be closed 0,5 (C)

from (C) to pass to open 0,3 (O)

and to stay O is 0,9

Then the probability of the sequence of states COO is

P (COO) = 0,5 * 0,3 * 0,9

P (COO) = 0,135

b) If people are either infected or susceptible, then

Probability of an individual infected is 0,5

Probability of an individual susceptible is 0,5

to pass from susceptible to infected is 0,05

to pass from infected to susceptible is 0,12

then

P ( SISI) = 0,5 * 0,05*0,12*0,05

P ( SISI) = 0,00015

probability for the following sequence of states COO