Math Is Fun Forum

Greaterpathmagician

Member

Registered: 2009-06-16

Posts: 32

Simulations

Hello

Can I please have help with the following question:

The Shy Family

A breakfast ceral company is having a special promotion. They are gibing away a figurine in every pack. There are six figurines to collect: Ashy, Bishy, Cashy, Dishy, Eshy and flushy.

Design a simulation to determine how many packets of cereal you would need to buy to collect all 6 figurines.

1.Each packet has only one figurine
2. You cannot swap figurines with other people
3. You may not onpern packets without buying them
4. Every figurine has ann equal chance of behing in a packet

Prompt questions: What is the probability of getting the six figurines in less than ten packests? 20 packets.

Extend this in some way.

What is the most suitable simulation I should do and how do I set it out.

Thank you

Help is greatly appreciated

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Simulations

Let

be the random variable for the number of packets needed to collect all six figures. Then

And

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Simulations

Hi;

Design a simulation to determine how many packets of cereal you would need to buy to collect all 6 figurines.

It is possible that you might have to buy an infinite number of boxes. Your question should read what is the expected number of boxes. This is an important point. If you do not understand what I mean by expected number then google for it.

The answer follows.

This is a well known probability problem called the coupon collector problem. The answer is derived from the Harmonic series.

So the expected number of boxes is 14.7.

If you need some pseudocode to program a simulation to test this, post and I will provide it.

Last edited by bobbym (2009-11-02 07:16:22)

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