Question

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.

Answer 1

Answer:

Depends

Step-by-step explanation:

Say that the 1000 people are people whose ages range from 1 to 100.

There is a 1/10 chance that the card given will be 1 to 100, and the person would have another 1/100 of getting their age AND card number matched.

So, we do 1/10 * 1/100 to get 1/1000 for a match.

This is only for if the people are 1 to 100 years old, so if it says something else, use this formula:

Probability = 1/10 * 1/highest age

Hope this helped!

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Answer 2

The probability shows that the expected number of cards given to people whose age matches the number on the card is 1.

How to compute the expected value?

From the information, a set of 1000 cards, numbered 1 through 1000, are distributed among 1000 people.

Let x be the random variable that's equal to the number of people who get a card.

Since we are looking for the expected value, this will be:

= E(X1 + X2 + .... X1000)

= 1

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