import math

lambd = 1.2

# 1.p(X = 2 ) 
k = 2
q_1 = (math.e ** (-lambd) * lambd ** k) / math.factorial(k)
print(round(q_1,2))

# 2.p (x < 3)
#  sum(x: 1-> 2)(possion(x, 1.2))
q_2 = sum([(math.e ** (-lambd) * lambd ** k) / math.factorial(k) for k in [0,1,2]])

print(round(q_2,2))

# 3p(x = 5) for /10 pages
lamdbd_ = lambd * 10
k = 5
q_3 = (math.e ** (-lamdbd_) * lamdbd_ ** k) / math.factorial(k)
print(round(q_3,2))


lamdbd_ = lambd * 40
q_4 = sum([(math.e ** (-lamdbd_) * lamdbd_ ** k) / math.factorial(k) for k in [0,1,2,3]])
print(1 -round(q_4,2))