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MrRa [10]
3 years ago
13

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 micros

econd; 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.
Mathematics
1 answer:
iragen [17]3 years ago
4 0

Answer:

a)  P (COO)  = 0,135

b) P ( SISI) = 0,00015

Step-by-step 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

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Answer:

Find the explicit from for the sequence t_n=t_{n-1}+4,t=6:

a_n=4n+2

This next question I edited a bit.  Your question just says find the four terms.  I'm assuming they meant the first four. I also changed the c to an a.

Find the first four terms of the sequence given by: a_n=n a_{n-1}-3,a_1=2:

a) 2,1,0.-3

You might want to read that second question again because there is errors in the question or things that don't really make sense.  I made my own interpretation of the problem based on my own mathematical experience.

Step-by-step explanation:

So your first question actually says that you can find a term by taking that term's previous term and adding 4.

So more terms of the sequence starting at first term 6 is:

6,10,14,18,....

This is an arithmetic sequence.  When thinking of arithmetic sequences you should just really by thinking about equations of lines.

Let's say we have this table for (x,y):

x  |   y

----------

1      6

2    10

3     14

4     18

So we already know the slope which is the common difference of an arithmetic sequence.

We also know point slope form of a line is y-y_1=m(x-x_1) where m is the slope and (x_1,y_1) is a point on the line.  You can use any point on the line. I'm going to use the first point (1,6) with my slope=4.

y-6=4(x-1)

y=6+4(x-1)    :I added 6 on both sides here.

y=6+4x-4     :I distribute here.

y=4x+2        :This is what I get after combining like terms.

So a_n=y and x=n so you have:

a_n=4n+2

---------------------------------------------------------------------------------------

The first four terms of this sequence will be given by:

a_1,a_2,a_3,a_4

a_1=2 so it is between choice a, c, and d.

a_n=na_{n-1}-3

To find a_2 replace n with 2:

a_2=2a_{1}-3

a_2=2(2)-3

a_2=4-3

a_2=1

So we have to go another further the only one that has first two terms 2,1 is choice a.

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