Probability from a Sample Space Practice Problem

This data science coding problem helps you practice Probability Fundamentals, probability from a sample space, and implementation skills. Read the problem statement, write your solution, and strengthen your understanding of Probability Fundamentals.

• Problem ID: 219
• Problem key: 219-probability-from-a-sample-space
• URL: https://datacrack.app/solve/219-probability-from-a-sample-space
• Difficulty: easy
• Topic: Probability Fundamentals
• Module: Probability

Problem Statement

# 🧩 Probability from a Sample Space

---

### 🎯 Goal

Calculate the probability of an event when every outcome in the sample space is equally likely.

---

### 📖 Introduction

A **random experiment** is something where the result is uncertain before it happens.

Examples:

- rolling a die
- flipping a coin
- drawing one card

Each possible result is called an **outcome**.

The set of **all possible outcomes** is called the **sample space**, written as:

$$
\Omega
$$

For example, when rolling one fair six-sided die, the only possible outcomes are 1, 2, 3, 4, 5, and 6. Therefore, the sample space is:

$$
\Omega = \{1,2,3,4,5,6\}
$$

An **event** is a group of outcomes from the sample space that match something we are interested in.

For example, the event "roll an even number" contains all even outcomes:

$$
A = \{2,4,6\}
$$

If all outcomes are equally likely, then:

$$
P(A)=\frac{|A|}{|\Omega|}
$$

---

### 🔍 Explanation of Symbols

| Symbol | Meaning |
|:--:|:--|
| $\Omega$ | sample space, the set of all possible outcomes |
| $A$ | event, the set of favorable outcomes |
| $\lvert A\rvert$ | number of outcomes in event $A$ |
| $\lvert \Omega\rvert$ | total number of outcomes in the sample space |
| $P(A)$ | probability that event $A$ happens |

---

### 📥 Input


- `sample_space`: a non-empty set containing all possible outcomes.
- `event`: a set of favorable outcomes. It must be a subset of `sample_space`.

### 📤 Output

- Return the probability of the event rounded to 6 decimals.

---

### 💻 Task

Implement `event_probability(sample_space, event)`.

Your function should:

1. Count the outcomes in `event`.
2. Count the outcomes in `sample_space`.
3. Calculate:

$$
P(A)=\frac{|A|}{|\Omega|}
$$

4. Return the probability rounded to 6 decimals.

---

### 🧩 Starter Code

```python
def event_probability(sample_space, event):
    pass
```

---

### 💡 Example

```python
event_probability(
    sample_space={1, 2, 3, 4, 5, 6},
    event={2, 4, 6}
)
```

Expected output:

```python
0.5
```

---

### ⚠️ Common Mistakes

- Dividing by the size of the event instead of the sample space.
- Providing an event containing outcomes outside the sample space. By definition, an event must be a subset of the sample space.
- Forgetting that probability is favorable outcomes divided by all possible outcomes.

Starter Code

def event_probability(sample_space, event):
    pass

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