# Arup Guha
# 7/15/2013
# Edited on 2/5/2020 for COP 2930
# Calculates the probability of getting a particular dice roll.

def main():

    # Print out dice chart.
    n1 = int(input("How many sides on your first die?\n"))
    n2 = int(input("How many sides on your other die?\n"))

    # Print out all ordered pairs of dice rolls.
    for i in range(1,n1+1):
        for j in range(1, n2+1):
            print("("+str(i)+","+str(j)+")", end="\t")
        print()

    # Calculate the probability of rolling a particular sum by
    # going through each possible dice roll.
    desired = int(input("What value do you want to roll?\n"))
    cnt = 0
    for i in range(1,n1+1):
        for j in range(1, n2+1):
            if i+j == desired:
                cnt = cnt+1

    print("Probability of getting", desired,"is",cnt/(n1*n2))
                
    # Calculate the probability of rolling a particular sum.
    # Efficient without a nested loop.
    cnt = 0
    for i in range(1,n1+1):
        if desired-i >= 1 and desired-i <= n2:
            cnt = cnt+1

    print("Probability of getting", desired,"is",cnt/(n1*n2))

main()