Question: I need help solving the following problem ! Bio statistics based on calculus ! Thank you so much! A molecule can enter or exist a

I need help solving the following problem ! Bio statistics based on calculus ! Thank you so much!

A molecule can enter or exist a cell within a one-minute period. If the molecule is inside the cell, it exits during a one-minute period with probability 0.2. If the molecule is outside the cell, it enters the cell during a one-minute period with probability 0.4. a. Let Pt be the probability that the cell is inside at time t. Write the dynamical system Pm in terms of Pt b. Assuming that the molecule is inside the cell at time t=0, what is the probability that the molecule will be Inside the cell at time t=2? c. Determine the long-term probability that the molecule is inside the cell. d. Suppose that the molecule is within the cell at time t=0. What is the probability that the molecule NEVER leaves the cell in the time interval between 0 and 3? (jm; think that the molecule does not leave at t=1 8: does not leave at t=2 St does not leave at t=3)

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