Battle Of The Sexes Write Up Essay

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Battle of the Sexes Case
Assignment 5

Battle of the Sexes

From
Group

Section 61

Date

May 4, 2015

Executive Summary
In Battle of the Sexes we are to determine the probability of three different scenarios based on a family with two children. We have solved each problem both analytically and by a Monte Carlo simulation.
Model
Main Objective: Given a family with two children, determine the probability of the following scenarios both analytically and by Monte Carlo simulation:
a. What are the chances that both of them are boys?
b. What are the chances that they have two boys, if we know that the older child is a boy?
c. What are the chances that they have two boys, if you know that they have at least one boy?
Structure
We first used Bayes Rule, a probability tree, and a probability list to solve the problem analytically.
Bayes Rule: P(G|B) = P(B|G)*P(G)/P(B)
P(B)=.5

P(G)=.5

a. P(B and B) = P(B)*P(B )=.5*.5 = .25
b. P(B2 given B1) = .5*.5/.5 = .5
c. P(B2 given B1) + P(B1 given B2) = See probability list
Here are decision trees we used:
a. What are the chances that both of them are boys?

b. What are the chances that they have two boys, if we know that the older child is a boy?

d. What are the chances that they have two boys, if you know that they have at least one boy?

Here is a view of the problems through the use of a probability list:
A.
0.25

Child 1
Girl
Girl
Boy
Boy

Child 2
Girl
Boy
Girl
Boy

B.
0.5

Child 1
Girl
Girl
Boy
Boy

Child 2
Girl
Boy
Girl
Boy

Child 1
C.
Girl
0.333333 Girl
Boy
Boy

Child 2
Girl
Boy
Girl
Boy

Monte Carlo Simulation
Then we conducted a Monte Carlo simulation using 1000 simulated scenarios. The simulation randomly assigned the gender of the first and

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