# -*- coding: utf-8 -*-

# MSPA 400 Session #4 Python Module #2

# Reading Assignment:

# “Think Python” 2nd Edition Chapter 5 (5.1-5.12)

# “Think Python” 3rd Edition Chapter 5 (pages 49-57)

# Module #2 extends set operations presented in Module #1. Probability rules

# are applied to sets. The rules are presented in Lial Sections 7.2-7.6.

# Generate the universe U. Note that range(1,27,1) will be used to produce

# a list of 26 positive integers for set operations. Remember, range()

# includes the first, i.e. 1, but not the last element, i.e. 27. The third

# argument, 1, defines the step used between consecutive elements. Note that

# the functions used in this module are available from Python itself.

U=range(1,27,1)

# Slice the list U into three subsets. Note that slicing is inclusive of the

# first indexed element and exclusive of the last indexed element. Also, the

# first element has 0 for an index.

A=U[0:13]

B=U[13:]

C=U[7:20]

A=set(A)

B=set(B)

C=set(C)

U=set(U)

print ('The universe U is %s ') %U

print ('\nA is %s') %A # Compare these sets to the slice statements above.

print ('B is %s') %B

print ('C is %s\n') %C

# It is assumed in this module that each element of U occurs with equal

# probability as would be the case with random sampling with replacement.

# This assumption allows the probability of a set to be calculated as the

# ratio of the length of the set (i.e. number of elements) divided by the

# overall length of U which in this Module is 26. Note that %r and %s both

# can be used with strings and lists.

# Convert the length of T to floating point to avoid interger division.

# The function round() was defined in earlier modules as was float().

T=float(len(U))

# Demonstrate the null intersection and probability.

Null=A&B

print ('Probability of null intersection %r \n') %round((len(Null)/T),3)

# Demonstrate the Union Rule for Probability.

print ('Intersection of A and C is %r') %(A&C)

print ('Union of A and C %s\n') %(A|C)

P=(len(A) + len(C) -len(A&C))

print ('Probability of A union C = %r \n') %round((len(A|C)/T),3)

print ('Result of Union Rule Summation = %r\n') %round((P/T),3)

# Demonstrate the calculation of Odds using the complement rule.

print ('Complement of C is %r') %(U-C)

print ('Odds of C are %r\n') %round((len(C)/float(len(U-C))),3)

print ('Complement of A intersection C is %r') %(U-(A&C))

P=(len(A&C)/float(len(U-(A&C))))

print ('Odds of A intersection C are %r\n') %round(P,3)

# Demonstrate conditional probability.

P=round(len(A&C)/float(len(C)),3)

print ('Conditional probability of A given C is %r') %P

# Demonstrate the product rule.

print ('Probability of A and C intersection is %r') %round((len(A&C)/T),3)

Q=len(C)/T

print ('Probability of C is %r') %round(Q,3)

print ('Product rule result for A and C intersection is %r') %round(P*Q,3)

# Exercise: Refer to Section 7.6 of Lial. Using the sets defined above and

# set operations apply Bayes' Theorem. Calculate the conditional

# probability of A given C, and the probability of C given A.