Bayes' Theorem - Lab

Introduction

In this lab, you'll practice Bayes' Theorem in some simple word problems.

Objectives

In this lab you will be able to:

• Use Bayes' theorem to determine the probability of specific events

Define a custom function for Bayes' theorem

To start, write a function, bayes(), which takes in the probability of A, the probability of B, and the probability of B given A. From this, the function should then return the conditional probability of A, given that B is true.

def bayes(P_a, P_b, P_b_given_a):
    # Your code here
    return P_a_given_b

Skin Cancer

After a physical exam, a doctor observes a blemish on a client's arm. The doctor is concerned that the blemish could be cancerous, but tells the patient to be calm and that it's probably benign. Of those with skin cancer, 100% have such blemishes. However, 20% of those without skin cancer also have such blemishes. If 15% of the population has skin cancer, what's the probability that this patient has skin cancer?

Hint: Be sure to calculate the overall rate of blemishes across the entire population.

# Your code here

0.46875

Children (I)

A couple has two children, the older of which is a boy. What is the probability that they have two boys?

# Your solution P(2boys|older child is a boy)

0.5

Children (II)

A couple has two children, one of which is a boy. What is the probability that they have two boys?

# Your solution P(2boys|1 of 2 children is a boy)

0.3333333333333333

A diagnostic test

A diagnostic test is advertised as being 99% accurate

• If a patient has the disease, they will test positive 99% of the time

• If they don't have the disease, they will test negative 99% of the time

• 1% of all people have this disease

If a patient tests positive, what is the probability that they actually have the disease?

# Your solution P(Disease | positive test)

0.5

Summary

In this lab, you practiced a few simple examples of Bayesian logic and how you can add prior information to update your beliefs about the chance of events.