**Expected value calculator** is a tool that helps users determine the **expected value (EV)** of a particular event or situation. The expected value is a **statistical concept** that represents the **average outcome** of a random variable.

## Expected Value Calculation Chart

Outcome | Probability | Value | Expected Value (EV) |
---|---|---|---|

Heads | 0.5 | $10 | $5 |

Tails | 0.5 | $0 | $0 |

Total for 1 Flip | 1.0 | $5 | |

Outcome (2 Flips) | |||

2 Heads | 0.25 | $20 | $5 |

1 Head, 1 Tail | 0.5 | $10 | $5 |

2 Tails | 0.25 | $0 | $0 |

Total for 2 Flips | 1.0 | $10 | |

Outcome (3 Flips) | |||

3 Heads | 0.125 | $30 | $3.75 |

2 Heads, 1 Tail | 0.375 | $20 | $7.5 |

1 Head, 2 Tails | 0.375 | $10 | $3.75 |

3 Tails | 0.125 | $0 | $0 |

Total for 3 Flips | 1.0 | $15 |

Single Flip: The expected value for a single coin flip is calculated as: EV = (0.510) + (0.50) = 5Two Flips: The expected value for two flips is calculated as: EV = (0.2520) + (0.510) + (0.25 * 0) = 5 + 5 + 0 = 10Three Flips: The expected value for three flips is calculated as: EV = (0.12530) + (0.37520) + (0.37510) + (0.1250) = 3.75 + 7.5 + 3.75 + 0 = 15

This format presents the formulas in a straightforward manner, making it easy to understand the calculations involved in determining the expected value for each scenario.

## Expected Value Formula

The formula for calculating expected value is:

**Expected Value (EV) = Σ (Probability of Outcome × Value of Outcome)**

Where:

**Σ**represents the sum of all possible outcomes**Probability of Outcome**is the likelihood of a particular outcome occurring**Value of Outcome**is the monetary or other value associated with that outcome

For example, let’s say you are considering investing in a stock with the following possible outcomes and probabilities:

Outcome A: Stock price increases by20%, with a probability of0.6Outcome B: Stock price decreases by10%, with a probability of0.4

To calculate the expected value of this investment, we would use the formula:

**EV = (0.6 × 20%) + (0.4 × -10%) = 12% - 4% = 8%**

**The expected value of this investment is 8%, meaning that on average, you can expect to see an 8% return on your investment.**

## What is the Expected Value in a Probability Calculator?

The **expected value** in a probability calculator refers to the **average** or **anticipated outcome** of a random event or process. It is calculated by multiplying the probability of each possible outcome by its corresponding value, and then summing these products.

The expected value provides a measure of the **central tendency** of a probability distribution, indicating the average or typical value that one can expect to occur over the long run. It is a useful metric for decision-making, as it allows individuals or organizations to weigh the potential **risks** and **rewards** of different options.

For example, let’s say you are considering playing a game where you can win

$100with a30% probability, or lose$50with a70% probability. The expected value of this game would be calculated as follows:

**Expected Value = (0.3 × $100) + (0.7 × -$50) = $30 - $35 = -$5**

The **negative expected value** of **-$5** indicates that, on average, you can expect to lose **$5** by playing this game. This information can help you make an informed decision about whether or not to participate in the game, based on your **risk tolerance** and **financial goals**.

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