#2.10
import random
omegaLUL = ['1']*2+['0']*6
n,m = 0,0
N = 10000
print(omegaLUL)
for i in range(N):
    for i in range(8):
        random.shuffle(omegaLUL)
    print(omegaLUL)
    for i in range(7):
        if omegaLUL[i] == '1':
            if omegaLUL[i+1] == '1' or (omegaLUL[0] == omegaLUL[7] == '1'):
                n+=1
print(n/N)

#########################################################################################

#2.11
import random
omegaLUL = ['1']*2+['0']*6+["2"]*4
n,m = 0,0
N = 10000
print(omegaLUL)
for i in range(N):
    for i in range(12):
        random.shuffle(omegaLUL)
    print(omegaLUL)
    for i in range(11):
        if omegaLUL[i] == '1':
            if omegaLUL[i+1] == '1' :
                n+=1
print(n/N)

#########################################################################################

#2.12
import random
omegaLUL = ['1']*2+['0']*8
n,m = 0,0
N = 1000000
for _ in range(N):
    new_lst = omegaLUL.copy()
    random.shuffle(new_lst)
    a = new_lst.index("1")
    new_lst[a] = "NEEDED"
    b = new_lst.index("1")
    if abs(a - b) <= 3 :
            n += 1
print(n/N)

#########################################################################################

#2.15
import random
omegaLUL = ["1", "2", "3", "4", "5", "6"]
n,m = 0,0
N = 10000
print(omegaLUL)
for i in range(N):
    a = []
    for i in range(4):
        a += [random.choice(omegaLUL)]
    if "6" in a:
        n+=1
    if "6" in a:
        a.remove("6")
        if "6" in a:
            m+=1
print(n/N)
print(1-(n/N))
print(m/N)

#########################################################################################

#2.16
import random
omegaLUL = ["0","1","2","3","4","5","6","7","8","9"]
n,m,b = 0,0,0
N = 1000000
for i in range(N):
    a = []
    for i in range(7):
        a += [random.choice(omegaLUL)]
    if a[-1] == a[-2] == a[-3] == a[-4]:
        n+=1
    if a[0]=="5":
        m+=1
    if ("5" in a) and ("1" in a) and ("2" in a):
        a.remove("5")
        a.remove("1")
        a.remove("2")
        if ("5" in a) and ("1" in a) and ("2" in a):
            a.remove("5")
            if ("5" in a):
                b+=1
print(n/N)
print(m/N)
print(b/N)

#########################################################################################

#2.17
import random
omegaLUL = [i for i in range(366)]
omegaLUL.remove(0)
n,m,b = 0,0,0
N = 10000
for i in range(N):
    a = []
    for i in range(12):
        a += [random.choice(omegaLUL)]
    for i in range(len(omegaLUL)):
        for j in range(i + 1, len(omegaLUL)):
            if omegaLUL[i]== omegaLUL[j]:
                n+= 1

print(n/N)