#1593 add the calculation script for 5.4-5

scripts/calculations/5.4-5.py

@@ -0,0 +1,21 @@
+import math
+
+
+def probability_exactly_i_pairs_have_matching_birthdays(i, k, n):
+    return math.factorial(k) / n ** k * math.comb(n, i) * math.comb(n - i, k - 2 * i) / 2 ** i
+
+
+def probability_k_people_have_same_birthday(k, n):
+    prob = 1.0
+    for i in range(0, k // 2 + 1):
+        prob -= probability_exactly_i_pairs_have_matching_birthdays(i, k, n)
+    return prob
+
+
+n = 365
+k = 3
+while probability_k_people_have_same_birthday(k, n) < 0.5:
+    k += 1
+print("""minimum number of people for which the probability\
+that three people have the same birthday\
+is at least 1/2:""", k)