Merge branch 'master' of bitbucket.org:vishap/test

puzzles/probability/problem.2.11.py

@@ -0,0 +1,41 @@
+
+import random
+
+# Problem:
+# 2.11
+# At a completely random moment between 6:30 and 7:30 a.m.,
+# the morning newspaper is delivered to Mr. Johnson’s residence.
+# Mr. Johnson leaves for work at a completely random moment
+# between 7:00 and 8:00 a.m. regardless of whether the newspaper 
+# has been delivered. What is the probability that Mr. Johnson can 
+# take the newspaper with him to work? Use computer simulation to 
+# find the probability.
+#
+# Solution:
+#      Applying Bayes' theorem.
+#      Newsletter arrives in interval 6:30 - 7:00 ?
+#          yes| p=0.5                    no| p=0.5
+#             |              Mr. Jonhnson leaves in interval 7:00 - 7:30
+#             |                      yes| p=0.5             no| p=0.5
+#             |             Newsletter arrives first in       |
+#             |                 interval 7:00-7:30            |
+#             |                yes| p=0.5       no| p=0.5     |
+#             |                   |                           |
+#            0.5     +       0.5*0.5*0.5      +            0.5*0.5 = 0.875
+#
+# Simulation:
+#       0.874867
+#       0.874876
+#       0.874876
+#
+
+newspaper_arrived_on_time = 0
+samples = 10000000
+for i in range(samples):
+    n = random.random()
+    w = random.random() + 0.5
+    if w >= n:
+        newspaper_arrived_on_time += 1
+
+print('simulated probability of ontime arrived newspaper is : {}'
+      .format(newspaper_arrived_on_time/samples))