# Expected Number of Age-Matching Cards in a Set of 1000

• succubus
In summary, probability is the measure of the likelihood of an event occurring and is typically expressed as a number between 0 and 1. It is calculated by dividing the number of desired outcomes by the total number of possible outcomes. There is a difference between theoretical and experimental probability, with the former being based on mathematical calculations and the latter being based on actual data. Probability and statistics are closely related, with probability being used in statistics to make predictions and draw conclusions from data. In real life, probability is used in various areas such as weather forecasting, sports predictions, and everyday decision making.
succubus
A set of 1000 cards, numbered 1 through 1000 are distributed among 1000 people. Compute the expected number of cards that are given to people whose age matches the number on the card.

So the relevant formula is expected value, but its conditioned because of the ages. So I assumed that the age range was between 1-100.
So n* P{card reads age | age <= 100)

Is this the correct assumption?

So would the probability be 1/1000 / 100/1000 = .01

Hints:

Consider the random variable N_i = number of people age i who get a card with their age.

We want E(N_1 + N_2 + ... + N_1000).

## 1. What is probability?

Probability is the measure of the likelihood that an event will occur. It is typically expressed as a number between 0 and 1, with 0 representing impossibility and 1 representing certainty.

## 2. How is probability calculated?

Probability is calculated by dividing the number of desired outcomes by the total number of possible outcomes. This can be represented as a fraction, decimal, or percentage.

## 3. What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability is based on actual data from repeated trials and may differ from theoretical probability.

## 4. What is the relationship between probability and statistics?

Probability is a branch of mathematics that deals with predicting the likelihood of events. Statistics is the science of collecting, analyzing, and interpreting data. Probability is often used in statistics to make predictions and draw conclusions based on data.

## 5. How is probability used in real life?

Probability is used in many areas of life, such as weather forecasting, sports predictions, and risk assessment in insurance and finance. It is also used in everyday decision making, such as choosing the most likely route to take when driving based on traffic patterns.

• Calculus and Beyond Homework Help
Replies
4
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
18
Views
2K
• Precalculus Mathematics Homework Help
Replies
2
Views
838
• Calculus and Beyond Homework Help
Replies
23
Views
2K
• Calculus and Beyond Homework Help
Replies
3
Views
711
• Calculus and Beyond Homework Help
Replies
4
Views
2K
• Calculus and Beyond Homework Help
Replies
2
Views
4K
• Calculus and Beyond Homework Help
Replies
6
Views
2K
• Calculus and Beyond Homework Help
Replies
21
Views
1K
• Biology and Medical
Replies
14
Views
2K