Problem Statement
The correct answer to this problem is worth 10 points.
You roll a standard 6-sided die three times in a row.
Theory
Probability of an Event
In Simple Terms 🧸
Probability is simply a way to measure chance. Imagine a bag with 10 marbles: 7 blue and 3 red. The chance of drawing a red marble is 3 out of 10. This is its probability. It shows what fraction of all possible outcomes is favorable to us.
Formal Definition 🎓
Probability is a numerical measure of the likelihood of a random event occurring. For the classical definition, where all elementary outcomes are equally likely, the probability of an event (A) is calculated as the ratio of the number of outcomes favorable to the event ((m)) to the total number of possible outcomes ((n)).
The value of a probability is always in the range from 0 (impossible event) to 1 (certain event).
Application in ML and Data Analysis 🤖
This is the foundation of everything.
- Classification: A model determines the probability that an email is spam. If (P(\text{spam}) > 0.8), the email is sent to the "Spam" folder.
- Scoring: A banking model calculates the probability that a client will default on a loan. A decision on loan issuance is made based on this value.
Output Format and Question
What is the probability that you will roll at least one six?
The answer must be presented as a decimal fraction with four digits after the decimal point, for example, 0.3145.