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### Course: Statistics and probability > Unit 7

Lesson 4: Experimental probability# 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 $1$ : $96565{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}05007{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}16605{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}81194{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}14873{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}04197{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}85576{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}45195$

Line $2$ : $11169{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}15529{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}33241{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}83594{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}01727{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}86595{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}65723{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}82322$

Things to know about random digit tables:

- Each digit is equally likely to be any of the
digits$10$ through$0$ .$9$ - 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
just to make them easier to read. The groups and rows have no special meaning. They are just a long list of random digits.$5$

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

Line $1$ : $\text{}96565{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}05007{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}16605{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}81194{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}14873{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}04197{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}85576{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}45195$

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

Line $2$ : $\text{}11169{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}15529{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}33241{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}83594{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}01727{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}86595{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}65723{\textstyle \phantom{\rule{0.167em}{0ex}}}{\textstyle \phantom{\rule{0.167em}{0ex}}}82322$

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