1. Amount of species in some population mayincrease some unit amount in a year or decrease the same amount withprobabilities 1/2 for each direction. Changes in different years areindependent. Zero amount correspond to embryo state which can change within ayear to unit amount with probability ½ or to negative unit which meanextinction of population forever.

a. Find probability of surviving ofpopulation for 10 years if at a starting moment population was at embryo state.

b. Find probability of survivingpopulation forever.

2.Two balls are distributed between 2 urns. At each step t of the process,one of the balls is chosen at random and transferred to the other urn. Numberof balls in urn 1 is considered as state of chain out of possible 3 states  { 0, 1, 2 }. At arbitrary t  we may observesome state St out of 3 possible with distribution p(t) ={ P (St =0), P( St=1), P( St =2 )} . Let at initial moment S0 =0 with probability 1. What can you say about distribution between states p(t) for a moment t when t is increasing?