# Simulation and randomness: Random digit tables

We can simulate events involving randomness like picking names out of a hat using tables of random digits. Tables of random digits can be used to simulate a lot of different real-world situations. Here's $2$ lines of random digits we'll use in this worksheet:

Line $1$: $96565\,\, 05007\,\, 16605\,\, 81194\,\, 14873\,\, 04197\,\, 85576\,\, 45195$

Line $2$: $11169\,\, 15529\,\, 33241\,\, 83594\,\, 01727\,\, 86595\,\, 65723\,\, 82322$

Things to know about random digit tables:

- Each digit is equally likely to be any of the $10$ digits $0$ through $9$.
- The digits are independent of each other. Knowing about one part of the table doesn't give away information about another part.
- The digits are put in groups of $5$ just to make them easier to read. The groups and rows have no special meaning. They are just a long list of random digits.

## Problem 1: Getting a random sample

There are $90$ students in a lunch period, and $5$ of them will be selected at random for cleaning duty every week. Each student receives a number $01-90$ and the school uses a random digit table to pick the $5$ students as follows:

- Start at the left of Line $1$ in the random digits provided.
- Look at $2$-digit groupings of numbers.
- If the 2-digit number is anything between $01$ and $90$, that student is assigned lunch duty. Skip any other $2$-digit number.
- Skip a $2$-digit number if it has already been chosen.

Line $1$: $~96565\,\, 05007\,\, 16605\,\, 81194\,\, 14873\,\, 04197\,\, 85576\,\, 45195$

## Problem 2: Doing a simulation

A cereal company is giving away a prize in each box of cereal and they advertise, "Collect all $6$ prizes!" Each box of cereal has $1$ prize, and each prize is equally likely to appear in any given box. Caroline wonders how many boxes it takes, on average, to get all $6$ prizes.

She decides to do a simulation using random digits as follows:

- Start at the left of Line $2$ in the random digits provided.
- Look at single digit numbers.
- The digits $1-6$ represent the different prizes.
- She ignores the digits $0, 7, 8, 9$.
- One trial of the simulation is done when all $6$ digits have appeared.
- At the end of the trial, she counts how many digits it took for every digit $1-6$ to appear (ignoring the other digits).

Line $2$: $~11169\,\, 15529\,\, 33241\,\, 83594\,\, 01727\,\, 86595\,\, 65723\,\, 82322$