Add Hamming Distance, Probability and Protein problems

10_iprb/iprb.nim

@@ -0,0 +1,38 @@
+import os
+import std/strutils
+
+let k = parseInt(paramStr(1))
+let m = parseInt(paramStr(2))
+let n = parseInt(paramStr(3))
+
+let T = k+m+n
+
+# Let "AA" be the case when we choose an individual with 2 dominant alleles,
+# "Aa" be the case when we choose an individual with 1 dominant and 1 recessive allele,
+# "aa" be the case when we choose an individual with 2 recessive alleles.
+#
+# Event probabilities:
+# p(AA) = k/T
+# p(Aa) = m/T
+# p(aa) = n/T
+# p(AA|AA) = (k-1)/(T-1)
+# p(Aa|AA) = m/(T-1)
+# and so on and so on.
+#
+# Choosing 2 individuals for mating is the combination of the probability events of choosing 2 individuals.
+# E.g., the probability of choosing two AA individuals is p(AA)*p(AA|AA) = (k/T)*((k-1)/(T-1))
+# Furthermore, for certain combinations, the probability that an offspring will display
+# the dominant phenotype is < 1. For example, when two Aa individuals mate, the probability of a dominant
+# phenotype is 0.75.
+
+let solution =
+    (k/T) * ((k-1)/(T-1)) +
+    (k/T) * (m/(T-1)) +
+    (k/T) * (n/(T-1)) +
+    (m/T) * (k/(T-1)) +
+    (m/T) * ((m-1)/(T-1)) * 0.75 +
+    (m/T) * (n/(T-1)) * 0.5 +
+    (n/T) * (k/(T-1)) +
+    (n/T) * (m/(T-1)) * 0.5
+
+echo $solution