(Solved): could you please help me with numbers 1&2 all the parts? thank you very much!! A. After 1 time s ...

A. After 1 time step, what is the probability that 2 particles have gone left and 2 have gone right? Give your answer as a decimal number between 0 and 1 to 3 decimal places. B. After 2 time steps, what is the probability that all of the particles are at the origin? Give your answer as a decimal number between 0 and 1 to 3 decimal places. C. After 2 time steps, what is the probability that none of the particles are at the origin? Give your answer as a decimal number between 0 and 1 to 3 decimal places. D. After two time steps, what is the probability that one or more particles are not at the origin? Give your answer as a decimal number between 0 and 1 to 3 decimal places. Problem 2 (1D random wall] Consider a large number of molecules starting at \( x=0 \) undergoing a 10 random walk fee. diffusing in 10). Each time step these molecules move a distance of 5 pm (either left or fichth. and the molecules move with a speed of \( 800 \mu \mathrm{m} / \mathrm{s} \). A. What is the diffusion coefficient for these molecules? Give your answer in units of \( \mu_{m}{ }^{2} / s \) B. After these molecules have undergone a random walk fie. diffused] for \( 0.5 \) seconds. what is the average \( x \)-position of a molecule in this cotlection? Give your answer in units of 1 im. C. After these molecules harve undergone a random walk fie. diffused) for \( 0.5 \) seconds, what is the rass-average distance from the starting location of a molecule in this collection? Give your arswer in units of prm. D. After \( 0.5 \) seconds, what is the farthest one of these molecules could possibly have traveled from the starting location? Give your actwer in units of \( \mu \mathrm{m} \). E. If initially there are \( 10^{26} \) molecules diffusing, how many have gone the maximum possible distance (most likely)?