Stat Trek

Teach yourself statistics

Teach yourself statistics

# Event Counter

The Event Counter counts the number of ways that two or more independent events can occur simultaneously (aka, the number of event multiples). For help in using the calculator, read the Frequently-Asked Questions or review the Sample Problem.

• Specify the number of independent events.
• Enter the number of possible outcomes for each independent event.
• Click the Calculate button to compute the number of event multiples.

## Problem

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### What is an event?

An event is a subset of a sample space - one or more sample points.

For example, suppose you flipped two coins. The sample space would consist of all possible outcomes from the toss of two coins - Heads/Heads, Heads/Tails, Tails/Heads, and Tails/Tails. A sample point would consist of a single outcome from the sample space - Heads/Heads, Heads/Tails, Tails/Heads, or Tails/Tails.

### What is an independent event?

In probability, two events are independent when the occurrence of one event does not affect the occurrence of the other event.

For example, suppose you rolled one die two times. The outcome of the first roll would be one event; the outcome of the second roll would be another event. The outcome of the first dice roll (Event 1) does not affect the outcome of the second dice roll (Event 2). Therefore, we would say each roll of a die is an independent event.

### What is an event multiple?

On this website, we refer to a grouping of two or more independent events as an event multiple. Many problems in statistics require a count of the number of unique event multiples that can be created from independent events.

For example, suppose one event is the outcome of a coin flip - heads or tails. Another event is the outcome from throwing a dart - hit or miss. These two events can be combined in four different ways - heads/hit, heads/miss, tails/hit, and tails/miss. Therefore, in this example, there are four possible event multiples.

This calculator, the Event Counter, counts the number of unique event multiples that can be created from two or more independent events. For an example that demonstrates event multiples, see the sample problem below.

## Sample Problem

1. On holidays, Chef Alice serves a dinner special consisting of a drink, an entree, and a dessert. Customers can choose from 5 drinks, 8 entrees, and 3 desserts. How many different meals can be created from the dinner special?

Solution:

The solution to this problem involves counting the number of event multiples. We know the following:

• Each dinner consists of 3 independent events - a drink, an entree, and a dessert.
• Customers can choose from 5 drinks, 8 entrees, and 3 desserts.

The number of event multiples would be (5)(8)(3) = 120. Thus, 120 different meals can be created from the dinner special. To solve this problem using the Event Counter, do the following:

• Enter "3" for "Number of independent events".
• Enter "5" for "Number of outcomes for Event 1".
• Enter "8" for "Number of outcomes for Event 2".
• Enter "3" for "Number of outcomes for Event 3".
• Click the "Calculate" button.

The answer, 120, is displayed in the "Number of event multiples" textbox, as shown below.