monte carlo techniques can be used to estimate the value of pi suppose you have round dart board that just fits inside of square cabinet if you throw darts randomlythe proportion that hit the dart board vs those that hit the cabinet (in the corners not covered by the boardwill be determined by the relative area of the dart board and the cabinet if is the total number of darts randomly thrown (that land within the confines of the cabinet)and is the number that hit the boardit is easy to show that write program that accepts the "number of dartsas an input and then performs simulation to estimate hintyou can use *random( to generate the and coordinates of random point inside square centered at ( the point lies inside the inscribed circle if < write program that performs simulation to estimate the probability of rolling five-of- -kind in single roll of five six-sided dice random walk is particular kind of probabilistic simulation that models certain statistical systems such as the brownian motion of molecules you can think of one-dimensional random walk in terms of coin flipping suppose you are standing on very long straight sidewalk that extends both in front of and behind you you flip coin if it comes up headsyou take step forwardtails means to take step backward suppose you take random walk of steps on averagehow many steps away from the starting point will you end upwrite program to help you investigate this question suppose you are doing random walk (see previous problemon the blocks of city street at each "stepyou choose to walk one block (at randomeither forwardbackwardleft or right in stepshow far do you expect to be from your starting pointwrite program to help answer this question write graphical program to trace random walk (see previous two problemsin two dimensions in this simulation you should allow the step to be taken in any direction you can generate random direction as an angle off of the axis angle random( math pi the new and positions are then given by these formulasx cos(angley sin(anglethe program should take the number of steps as an input start your walker at the center of grid and draw line that traces the walk as it progresses