## Situation Description
Imagine a medical study involving two groups of people:

- Group $$H$$: 750 individuals with **heart problems**;
- Group $$S$$: 800 individuals with **chronic stomachache**.

We know the following about diabetes prevalence:

- Among group $$H$$, 7% have diabetes — this is the conditional probability $$P(D∣H)=0.07$$, meaning the probability that a person has diabetes ($$D$$) given they have a heart problem ($$H$$);
- Among group $$S$$, 12% have diabetes — this is $$P(D∣S)=0.12$$, the probability of diabetes given stomachache.

Here, the letters represent:

- $$H$$: event "person has a heart problem";
- $$S$$: event "person has a stomachache";
- $$D$$: event "person has diabetes".

We want to analyze the overall population formed by these two groups combined.

Probability theory is a fundamental branch of mathematics that deals with the study of uncertainty and randomness. It provides a framework for understanding and quantifying uncertainty in various fields, including statistics, data analysis, machine learning, finance, physics, and more.

We will start our way of learning probability theory by considering some basic definitions and rules: what is a stochastic experiment and random event, what is independence and incompatibility of events in the context of probability theory, what is the probability and how can we calculate probabilities of different elementary events. 

In real-life tasks, we often have to deal with complex relationships and, as a result, calculate probabilities of several events or events that depend on each other. Let's consider how we can do this using probability theory.

To solve many real problems in probability theory, special models have been created that describe a particular situation. Let's consider some of the most used models that can be used to describe some discrete results of stochastic experiments.

What if the result of a stochastic experiment cannot be described by a discrete value? For this, models that work with continuous values are used. Consider the most popular of these models.

Often we are faced with the task of checking the dependence of the results of different stochastic experiments on each other. Moreover, it is necessary not only to assess the presence of dependencies but also to somehow quantify the degree of dependencies. To solve these problems, we can use covariance and correlation.

Challenge: Solving the Task Using Bayes' Theorem

Situation Description

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Challenge: Solving the Task Using Bayes' Theorem

Situation Description

Ratkaisu