feat: probability exercises

src/modules/probability.py

@@ -56,8 +56,49 @@ class BetaDistribution:
 	def calc_region(init_probability, end_probability, success_count, failure_count):
 		return BetaDistribution.calc(end_probability, success_count, failure_count) - BetaDistribution.calc(init_probability, success_count, failure_count)
 
+p_r = 0.3
+p_u = 0.4
 class Exercises:
+	@staticmethod
+	def one():
+		# 30% change of rain and 40% change your umbrella order will arrive. P(R AND U)
+		return p_r * p_u
 	
+	@staticmethod
+	def two():
+		# Same Ps as previous. P(!R OR U)
+		# RU !RU !R!U R!U
+		return (1 - p_r)  + p_u - ((1 - p_r) * p_u)
+
+	@staticmethod
+	def three():
+		p_u_given_rain = 0.2
+		return p_u_given_rain * p_r
+
+	@staticmethod
+	def four():
+		n = 137
+		p_bail = 0.4
+		p_at_least_50_bail = 0.0
+		for x in range(50, n + 1):
+			p_at_least_50_bail += binom.pmf(x, n, p_bail) 
+		return p_at_least_50_bail
+
+	@staticmethod
+	def five():
+		n = 10
+		h = 8
+		t = 2
+		return  1.0 - BetaDistribution.calc(0.5, 8, 2)
+
+	
+	@staticmethod
+	def test():
+		print("P(R AND U) = {0}".format(Exercises.one()))
+		print("P(!R OR U) = {0}".format(Exercises.two()))
+		print("P(U AND R) = {0}".format(Exercises.three()))
+		print("P(At least 50 bail) = {0}".format(Exercises.four()))
+		print("P(fair) = {0}".format(Exercises.five()))
 
 
 def test_probability_module():
@@ -67,3 +108,5 @@ def test_probability_module():
 	print(">> Beta distribution")
 	print(BetaDistribution.calc(0.9,8,2))
 	print(BetaDistribution.calc_region(0.8, 0.9, 8, 2))
+	print(">> Exercises")
+	Exercises.test()