Question

(1)Make a simulation program of the Galton board. Keep in mind that your program must be simulation-based. The positions of the ball will be determined by the random functions.

(i) Assume that this Galton board is an unbiased board. In other words, the ball will have equal probability of moving to the left or to the right (50% vs. 50%). This Galton board has 10 levels. There are 10000 balls to drop from the center of the top level. The program will finally output the simulated result: the distribution of the numbers of balls in each position at the bottom level.

(ii) Assume that this Galton board is slightly biased (or tilted). The ball will have 47% of chance of moving to the left when it hits any peg, and 53% to the right. This Galton board has 10 levels and you run the simulation for 10000 balls. The program should finally output the result of distributions at the bottom level.

need code in python with comments

Answer 1

Summary :

python code is pasted below which has comments inline and all the parameters can be changed at the begining of main program which go as input to the game .

Output for both 50,50 and 47,50 are shown as part of output .

Note : Input for bias require to be in decimals for eg [0.47, 0.50] for second case .

######################### Python Code ###########################

from random import choices

def get_next_position( current_level , current_position , probability) :
    # Define possible outcomes and respective probabilities
    outcomes = [0,1]
  
    # get randomly the output
    output = choices(outcomes , probability)
  
    next_position = current_level + current_position + output[0]

    return next_position
  

def cur_start( level ) :

    if level > 1 :
        return ( ( level - 1) + cur_start( level -1 ) )
    else :
        return 1 ;
      
  

if __name__ == '__main__':
    # Define Number of balls and levels
    num_balls = 10000
    num_levels = 10
    outcome_probability = [0.50 , 0.50]
  
    num_slots_bottom = num_levels + 1
  
    bottom_level = []
    for i in range(num_slots_bottom) :
        bottom_level.append(0)
      
    bottom_level_offset = int(1+ num_levels * (num_levels + 1 ) / 2)
    #print(" BottomLevel Offset " , bottom_level_offset)
  
    ## cur_pos - start with current position as level & cur_pos as 1 and start calculating level 2 position
    ##
    ##
    ##
    for cur_ball_num in range( num_balls ) :
        cur_pos = 1
      
        for level in range( 1 , 11 ):
            next_pos = get_next_position(level,cur_pos,outcome_probability)
            #print("Cur Pos : -> ", cur_pos , " Next Pos -> " , next_pos )
            cur_pos = next_pos
          
        # Increment ball count on the bottom level .
        #print(" Bottom level -> " , cur_pos , " Buttom count -> " , bottom_level[cur_pos - 56])
        bottom_level[cur_pos - bottom_level_offset] = bottom_level[cur_pos - bottom_level_offset] + 1
      
    print("( " + str(outcome_probability[0]*100) + "% , " + str( outcome_probability[1]*100) + "% )" )
    print(" Ball Count at Bottom Level : ")
    total_ball_count = 0
    for i in range(num_levels + 1):
        total_ball_count = total_ball_count + bottom_level[i]
        print(" slot : " , i , " --> ", bottom_level[i])
  
  
    print(" Total Ball Count : " , total_ball_count )

####################### End of Python Code #######################

#################### Output #####################################

usr@DESKTOP-VUMS 26N:/mnt/i/PRJ/Code/pyth$ python3 galton_board.py ( 47.0%, 53.0%) Ball Count at Bottom Level : slot: 0 --> 3 slot : 1 --> 62 slot : 2 --> 266 1 slot : 3 --> 902 slot : 4. --> 1801 slot : 5 --> 2460 slot: 6 --> 2261 slot : 7 --> 1470 slot : 8 --> 614 slot: 9 --> 142 slot : 10 --> 19 Total Ball Count : 10000 usr@DESKTOP-VUMS 26N:/mnt/1/PR/Code/pyth$ python3 galton_board.py (50.0%, 50.0%) Ball Count at Bottom Level : slot: 0 --> 9 slot : 1 --> 97 slot : 2 --> 394 slot: 3 --> 1161 slot: 4 slot: 5 2436 slot: 6 --> 2021 slot : 7 --> 1193 slot : 8 --> 471 slot: 9 --> 103 slot : 10 --> 9 Total Ball Count : 10000 usr@DESKTOP-VUMS 26N:/mnt/1/PRJ/Code/pyth$ --> 2146

#################### End Output #####################################