**Probability theory** explores randomness and uncertainty in math. It gauges the odds of outcomes in uncertain scenarios. Used in stats, ML, finance, physics, bio, and engineering.

## Why do we need probability theory?

Probability theory is commonly used to solve various real-life tasks: 
- **Uncertainty Modeling**: models and quantifies uncertainty, aiding decisions and predictions in real-world scenarios;
- **Statistics and Data Analysis**: underpins stats and data analysis. It offers tools for parameter estimation, hypothesis testing, and drawing data-based conclusions;
- **Machine Learning**: is vital in ML, including Bayesian methods, graphical models, and reinforcement learning;
- **Risk Assessment and Decision Making**: in finance and beyond, probability assesses risks, guides investments, and informs decisions amid uncertainty;
- **Experimental Design**: in scientific experiments, probability theory helps in designing experiments, analyzing data, and drawing reliable conclusions;
- **Natural Phenomena Modeling**: in physics and engineering, probability models and explains complex natural randomness.

## Why is this course included in the track?

Probability theory is vital for data scientists, aiding in uncertainty reasoning, data-driven choices, robust experiments, ML models, and insightful data interpretation. Proficiency in it is key for effective problem-solving and success.

### Example 

Calculate the probability that a randomly chosen man will have a height greater than 180 cm.


from scipy.stats import norm

# Parameters of the normal distribution
mean_height = 175  # Mean height in cm
std_dev_height = 5  # Standard deviation of height in cm

# Height threshold (greater than 180 cm)
height_threshold = 180

# Calculate the z-score for the height threshold
z_score = (height_threshold - mean_height) / std_dev_height

# Calculate the probability using the CDF of the normal distribution
probability = 1 - norm.cdf(z_score)

# Print the result
print(f'Probability is {probability}')

Here we will briefly describe all the courses on the track and consider how you can apply the gained knowledge in practice.

Preparation for Data Science Track Overview

Probability Theory Basics

Why do we need probability theory?

Why is this course included in the track?

Example